Extracts are really, really, weird. They are a (Su) ability, which normally don't provoke. No where in the class description does the RAW state that they provoke. However, the RAW does state:
"An extract is 'cast' by drinking it, as if imbibing a potion."
Potions do provoke. This would also seem to imply the Accelerated Drinker Trait would apply to Extracts. The APG FAQ states:
"It is a standard action to use an extract, mutagen, or throw a bomb. This action includes retrieving the necessary materials from the alchemist's supplies, in the same manner as retrieving a material component is included in the act of spellcasting."
This in not at all how potions work. They must be retrieved as a move action which provokes. This raises the question: which potion rules do extracts follow? Do they provoke, like potions; not, like (Su)s; or provoke, like spells?
Personally, I believe the RAI is for extracts to provoke, however that would leave no way for a Alchemist do "Drink Defensively" which would be a drawback for a Mr. Hyde type Alchemist. At least he can draw and use an extract as part of a standard action.