Actually this wasn't a fighter, but an RNZAF Short Sunderland, which provided an aviation lifeline to the island until it was holed by a rock while taking off from the Te Whanga Lagoon in 1959.
The air force sent a crew to remove the most valuable equipment, decided it would be too costly to fix and gave it to the island.
Two shrewd local farmers, the Wisener brothers, promptly took the 27m body to bits and used the material to make a couple of barns and a car body. The rest was left to lie forgotten in their paddocks.
But in the past few years a small tourist industry has developed and groups like ours turn up to visit the small settlement of Kaingaroa, check out the fur seals, explore the ruins of an early German mission settlement - and marvel at a flying boat in the bush.
Our guide to the Chathams, Val Croon jnr, pointed out where the rear fuselage was being used as a shed, the nose was lying in a field and part of the tail was in the trees.
It looked to me as though half a century on the whole plane was still there.
"It is," said Val. "In fact they're planning to put it back together."
Sure enough, around the corner the two keels had already been re-assembled inside a support frame.
I learned more about the project the following Sunday when we attended the 125-year-old St Augustine's Anglican Church, the oldest on the island, where one of the key players, Colin Barr, preached the sermon.
Also, project leader Gary Downs was running the Sunday school.
Gary, a pilot with Air Chathams, explained that this summer a crane would be used to fit the big sections together, a big pole shed would be built over the top and work would start on a museum of Chatham Islands aviation.
The plane's original engines were too badly corroded to restore but Fieldair of Palmerston North had provided one "in exchange for a box of chocolates", and propeller parts had been collected to restore a complete propeller unit.
To provide a human perspective a researcher is gathering the memories of "locals who flew on it, including some who were children at the time, and we've even found a couple of the crew".
The museum displays will also acknowledge the other aircraft which have served the island over the years, from Catalina flying boats and DC3s to Fokker Friendships and Bristol Freighters, not to forget the Convairs that Air Chathams uses at the moment.
As it happens, Gary was second officer on the Convair which flew us home after our holiday and I was thrilled to be allowed into the cockpit to watch the landing at Auckland Airport.
That excitement is why he feels the aviation museum will prove an asset to the Chathams.
"People are fascinated by flying and the Sunderland Short is a rare and special aeroplane with a lot of wonderful stories surrounding it. We think it's worth preserving and allowing others to share."
CHECKLIST
Further information: Pukekohe Travel run all-inclusive tours to the Chatham Islands. Phone 0800 785 386.
To contact the Sunderland restoration project email garyandgin@hotmail.com
Jim Eagles was taken to the Chatham Islands by Pukekohe Travel.
