This is untested and unfinished, so please feel free to criticise.
The Alchemist, or Natural Philosopher, is a scholar who specialises in the lore of potions. It might be objected that most such would not be adventurers. This is of course true, but it is equally the case that most priests and wizards are unlikely to live as wandering vagabonds, and likewise that most soldiers would be in an army and most thieves in a gang of other thieves.
Alchemists have the same XP requirements, Hit Points, weapon restrictions, and attacks as Magic-Users. However they may wear leather or chainmail armour, or any magical armour (platemail is too heavy for them), and may use shields. Their Prime Requisite is Intelligence.
Swords and Wizardry: Alchemists start with a Saving Throw of 15 like Magic-Users, but have no bonus against spells.
Fortitude, Reflex, Will: Alchemists have a good Fortitude save.
Basic/AD&D: Alchemists save as Fighters.
In all cases, Alchemists have a bonus against poison and intoxicants, including alcohol, equal to their level +1.
They start play with two potions, which are rolled randomly as if generating treasure.
In areas with the proper facilities (usually large towns and cities), they may make potions when not adventuring. It takes a week to attempt to make a potion.
The player may roll randomly as if generating treasure. This costs 500gp.
The player may also attempt to make a specific potion. Their chance of success is 10% times their level, to a maximum of 90%. Failure indicates that the player has wasted 250gp.
Alchemists may also attempt to identify potions. In a properly-equipped facility they can do so with certainty given a day, and 100gp spent. They may also try to identify a potion by taking a small sip. Their chance of success is 45%, plus 5% per level, to a maximum of 90%, secretly rolled by the DM. Failure indicates (equal chance of each) they accidentally drink too much (ie they drink the potion), they misidentify the potion (roll randomly for what they think it is), or they are unable to identify the potion.
Optionally the Alchemist may be given the ability to make miscellaneous magic items as well as potions.