Thought at one point to be headed for extinction, their numbers have recovered a little, but their future is by no means assured and few humans have ever seen one. But every now and again a fortunate handful of people get the chance to make the acquaintance of Sirocco, kakapo ambassador to the world, a role which has made him a star on YouTube, Twitter and Facebook.
I was lucky enough to meet Sirocco in Wellington during a mission to explore the capital's alternative nightlife. We've all heard about the city's cafes and restaurants. But there is also a darker world that comes to life when the sun goes down; a realm of earthquakes, giant squids, space rockets and aliens, ancient reptiles and rare birds.
My foray into this mysterious realm began at Te Papa on one of its Night At The Museum tours which - like the two Ben Stiller films of the same name - are pretty scary.
The light was already fading as Tony, my guide, led me upstairs into the gloom... and face to face with two vicious velociraptors with a nasty-looking pterodactyl flying overhead. Just round the corner, a Haast's eagle was about to grab a giant moa with its razor-sharp talons. Eeek.
They're in a display named Blood Earth Fire, which shows how seismic forces, waves of human migration and introduced animals have changed the landscape and wiped out dinosaurs and moa (and nearly kakapo).
Extinct or not, this was not a place I wanted to be when the museum came to life, so I headed for the safety of a nice little pioneer cottage. That turned out to be a case of off the dinner plate and into the blender, because no sooner had the door closed than the whole place started shaking.
I had fled into an exhibition called Awesome Forces which was all about the landslips, tsunami, volcanoes and earthquakes that are facts of life in NZ. Its sweeping catalogue of disaster, including the massive landslip which wiped out the village of Te Rapa on the shores of Lake Taupo in 1846, the Tarawera eruption of 1886, the 10m-high tsunami that hit Gisborne in 1947 and the earthquake in the Far North on Christmas Eve 1963, was hardly comforting.
Things didn't improve when Tony took me upstairs to Te Papa's marae, where a fierce warrior demonstrated how to maim enemies with a taiaha. It wasn't any more comfortable when I wandered into the Ka Mate exhibition to find myself facing another warrior who insisted I join in the haka. A few moments later, I was stamping feet and slapping thighs beside a tourist from Vancouver who panted, as he poked out his tongue defiantly, "I didn't know this was going to be interactive."
But the last straw came at the Mountains to the Sea exhibition, focused on our native animals and plants, where I scuttled under a vast pigmy blue whale skeleton - A pigmy? At 21m long? - only to end up before the soccer-ball-sized eyes of a colossal squid. It lay watchfully in its tank, eight massive arms seemingly poised to grab unwary bystanders.
The next stop was a late-night session at Carter Observatory, on a hilltop above the city centre and best reached via the Cable Car which, on a pitch-black night, felt like travelling in a spaceship.
That turned out to be quite appropriate, because the show in the planetarium was about the history of the space race, from the Soviet launch of the first Sputnik in 1957, to Yuri Gagarin becoming the first man in space in 1961, to the US putting Neil Armstrong and Buzz Aldrin on the moon in 1969.
The place was swarming with Scouts, who had a great time in the observatory's interactive displays on navigating by the stars, how the universe was formed, travelling through a black hole and the astronomical work of Captain James Cook.
But, for me, the most intriguing moment came at the end of the show when one of the Scouts asked the presiding astronomer: "Do you believe in aliens?" Instead of answering, he said: "There's a lot of questions, and if you're really interested in my answers, I'll talk to you later."
Hmm. Was that suspicious or what? My suspicions grew when it was announced the observatory's 23cm Cooke refractor telescope, dating from 1867, couldn't be used because of a mechanical fault. Instead, we'd have to gather outside under the stars.
I hung around, learning how to use the Southern Cross to find south and snatching a quick peek at the craters of the moon through a portable telescope. But you do hear of people being kidnapped by aliens, and the surrounding Wellington Botanical Gardens would be the perfect place to do it, so, before the flying saucers arrived, I boarded the Cable Car for the "flight back" to the bright lights.
The final leg of my mission involved a Wellington Night Tour which ended at the Zealandia wildlife sanctuary where, on a previous visit, I had seen a little spotted kiwi and a tuatara. But this visit was all about meeting Sirocco.
This is a bird described by Deidre Vercoe Scott, manager of the Kakapo Recovery programme, as "the perfect ambassador for his species. He picked himself in a sense. Because he was very sick when he was young, he had to be hand-reared and was strongly imprinted on humans. As a result, he doesn't interact with other birds but he does like to be around people."
For instance, she said, he hangs around the hut at his sanctuary on Maud Island, sometimes peers in the windows and, come mating time, "even builds his booming bowl between the hut and the longdrop where there is a lot of foot traffic".
Far from being stressed by his sessions with people, "he really enjoys them. You can tell he gets a lot from it. When the time comes, he's always waiting at the door of the enclosure keen to get started."
Certainly, as our group approached his glass-fronted enclosure, Sirocco was there to say hello, giving us an eyeful of his powerful body and magnificent green plumage. Then he lost interest, climbing on to a branch further away and turning his back on us.
He perked up when a guardian, Karen Ludwig, went inside to give him a macadamia nut. "Ah, yes," she said, as he smugly nibbled. "You know how to make me do what you want."
With a grape or two, she persuaded Sirocco on to the scales. "Goodness, 2.78kg. It's usually 2.7kg. How did that happen? No more treats for you, my boy."
But this is one smart kakapo. Swiftly, he had climbed on her shoulder, nuzzled her ear affectionately and was soon nibbling more grapes.
Then he generously consented to parade down the branch for us, and our 25-minute viewing session was over.
I lagged behind for one last photo and he posed perfectly, so I could get both the beautiful green tail feathers and his handsome profile. What a poser. No wonder Prime Minister John Key named him New Zealand's Official Spokesbird for Conservation.
CHECKLIST
Getting there: Air NZ has regular flights to Wellington.
Where to stay: The Bolton Hotel is a charming five-star boutique hotel in the heart of Wellington. It offers Wellington Night Tours, taking in the Carter Observatory and Zealandia.
Where to eat: Wellington has plenty of great restaurants, but if you want something cheap and cheerful, try one of the eateries at Left Bank, the notorious graffiti alley off Cuba Mall - especially Viva Mexico, where you could easily imagine you were at an old cantina.
What to do:
Visit Te Papa or the Carter Observatory.
Sirocco will be at Zealandia until October 31.
Jim Eagles met Sirocco with help from Air New Zealand and Positively Wellington Tourism.