He said it was "big enough to be really scary" - roughly 3.5 metres long.
"It was right on top of the water. Its fin was out of the water and you could see it looking at us and cruising around."
He used his paddle to knock it on the nose, hoping it would swim away.
"We were both a bit scared. I thought if we could get paddling in, either it will follow us or it won't and it's probably our best chance of getting away from it, so we pulled up our anchors and started paddling in."
Chase said it followed them for a little bit.
The ordeal lasted about 15 minutes. But once back on shore, it reappeared. Now, safely at home, they feel "lucky to be alive" and can't stop thinking about what happened.
"There's a sense of relief. It was surreal." They caught several kahawai during their three-hour fishing trip.
Department of Conservation marine scientist Clinton Duffy said from what the kayakers had described, it was "fairly typical" great white behaviour.
He said, although it could also have been a bronze whaler shark, they didn't grow to be more than 3.3metres. And 3.5 metres was an "average size" for a great white.
"They regularly investigate any large objects that are silhouetted against the surface to see if they are potential prey, including lumps of seaweed, seabirds, and boats. They also scavenge on whale carcases floating at the surface."
Duffy said while there were no particular "hotspot" areas for the creatures around the region, they tended to turn up in places that held "good numbers of fish", including the likes of trevally, king fish, snapper and hāpuku.
The protected species usually came through to the Hawke's Bay coast between May and November, but could be in the region's waters year-round, Duffy said.
"They are much less abundant than most other species but are regular visitors."
"... places like the mouth of the Mohaka River and recognised fishing spots could hold them for anywhere from a few days to a month or so."
Brown - a keen fisherman has seen smaller sharks over the past five years, but never one "anywhere near that size". While they plan on going out again, they will be a little bit more careful.
"I'm more inclined to go with someone else now".
Hawke's Bay's only fatal shark attack occurred on December 20, 1896, and claimed the life of Bright Cooper.
The attack, by what is believed to be a great white shark took place about 25 metres off Marine Parade beach.