Kakapo
Although most parrots are able to fly, they appear to prefer eating saltines while perched on pirates' shoulders. The kakapo, however, is an exception to this norm. It shouldn't surprise you in the least that this flightless parrot comes from New Zealand. It was given the scientific name Strigops habroptilus, which translates to "owl-face soft-feather". If you look at one face-on, you can see why; the kakapo has a heart-shaped face that resembles an owl's and does appear to be soft, but it's kind of a strange distinction because you could also say that about an ostrich.
The kakapo is the only flightless parrot, and unlike chickens, it doesn't even pretend to fly, according to Wired. Never does it flap its wings. They serve only as a means of balance and occasionally as a parachutist. The kakapo can climb trees and occasionally slows down when jumping to the forest floor by using its wings.
Kakapos are wonderful pets because they are sociable and don't require you to trim their wings. However, since kakapos and other flightless island birds are endangered, you cannot truly acquire one, only about 150 kakapos remain in the wild as of right now.