Gum drops restore a single hit points and cause a similar amount of radiation poisoning. While the box says "Radioactive", the gumdrops have a lower radiation count than other food items. Because of this, even a slight radiation resistance can negate this effect, rendering them harmless. Gum drops are one of the rarest consumables in the game.
At A Quick Fix in Rivet City. It must be stolen from the shop and does not appear to be for sale in the owner's inventory.
During Broken Steel, three can be found in the Mobile Base Crawler. One in the base floor behind a Repulsion Field along with other items, and one in the launch platform base, in the toilet cubicle which hasn't been flushed (and that an Enclave soldier has apparently been having some nasty problems involving the removal of his intestines after ingesting these). The third can be found at the southeast corner on the ground floor behind a Repulsion Field along with chems and other first aid supplies.
During Broken Steel one can be found in one of the Eat'o'tronic 3000s in Old Olney Underground.