Gum Drops

 are a food item found in Fallout 3. It can restore some of your Hit Points and causes no Radiation poisoning, but they are very rare. While it seems odd that the box says Radioactive Gumdrops and do not irradiate you, gumdrops actually provide radiation, but less than 1 rad per package. Since the in game description will only show whole rads, the game rounds down and displays no radiation at all.

Known Locations
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.

In the Jury Street Metro Station area (see Dead Man's Signal).

James Hargrave and C.J. Young carry them, they can be pickpocketed. Only with high Luck, they may also carry bubblegum.

In the Vault Theme for your Megaton house; one appears on the shelf with the food in.

During Broken Steel two 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).

During Broken Steel one can be found in one of the  Eat'o'tronic 3000s in Old Olney Underground.

Glitches
if you have a follower, (confirmed Charon) and you put the gum drops in their inventory, they vanish from the inventory.