Chems in "Fallout 2" can boost your stats, heal damage or restore Action Points, among other useful effects. However, many chems also carry a risk of addiction. Once you're addicted to a chem, going long enough without taking any of it will trigger withdrawal symptoms, which can inflict severe penalties. For Jet addiction, you need an antidote--the rest just take time.
Curing Most Addictions
Common chem addictions are like the common cold--the only cure is to wait a week. Withdrawal symptoms begin 48 hours after the last "fix" and end seven days later.
Curing Jet Addiction
Unlike other chems in the game, Jet causes permanent addiction. The only way to remove the addiction is with an antidote. Securing the antidote requires completing a quest. Two different quests can lead to the production of a Jet antidote. If you convince Myron, the Mordino family's drug chemist, that a cure for Jet is possible, he will ask for some endorphin blockers. Talk to Doctor Troy in Vault City about them and he will be able to produce a cure. Alternatively, if you visit Vault City first, Doctor Troy may ask the Chosen One to smuggle some Jet into the city so that he can synthesize a cure.
Regardless of which quest you take, the result is two doses of Jet antidote. Talk to Councillor McClure in Vault City; he will explain that one of the doses needs to go to Doctor Johnson in Redding. The other one will remain in your inventory and can be used to cure Jet addiction. The antidote is not consumed after use, giving an effectively infinite supply--and thus, ability to use Jet at will, without fear of addiction.