It's not in the rules. The USGA interpretation (FAQs) is as follows:
Rule 14-1
Using Club other than Putter on Putting Green?
Q. Is it permissible to use a club other than a putter to play a stroke on the putting green?
A. Yes,
the Rules of Golf do not stipulate the type of club that must be used
for making a stroke on the putting green or anyplace else on the golf
course.
In WGT, chipping from the green is a permissible stroke, but in my experience the chipping stroke does not function properly on the green, so there are plenty of spots (especially at St. Andrews) where it is definitely better to land on the fringe than just on the green.