I can't find anything saying the Alchemist needs rest to replenish his capacity to make Extracts. But then again, she's not a caster, so it'd make sense.
I'd just like to make sure I'm not missing something obvious.
An alchemist can create only a certain number of extracts of each level per day.
An extract, once created, remains potent for 1 day before losing its magic, so an alchemist must re-prepare his extracts every day.
Mixing an extract takes 1 minute of work — most alchemists prepare many extracts at the start of the day or just before going on an adventure, but it's not uncommon for an alchemist to keep some (or even all) of his daily extract slots open so that he can prepare extracts in the field as needed.
If no rest is needed, this also begs the question of "when does the day start?" Is it simply midnight?