Phil Mickelson has 5 majors to his name but some still consider him a choker given the number of times he has lost from a winning position, especially at the US Open.
Montgomerie also obviously failed to convert his Tour success into majors but I don't think he ever really choked (with the exception of his 2nd at the final hole of the 2006 US Open...although at that stage he didn't know that Mickelson would also have a meltdown) - he just never seemed to enjoy the rub of the green, pardon the pun, when he needed to.