A fresh carrot can restore some Hit Points, without irradiating the consumer. It is one of the few edible food items that doesn't give you any radiation, besides other fresh fruits or vegetables, and food found in a non-compromised vault.
The only place they can be found is in the Science Lab in Rivet City (eight in total), although taking them is considered stealing.
Fresh carrots and other fresh vegetables available in the Rivet City Science Lab are the direct result of the current Rivet City science project. There is a random bit of speech that may be told to the player from Janice Kaplinski that explains that they are the result of the work that is being undertaken in the lab.
The scientists at Rivet City have a large stock of fresh fruit and vegetables, and will say, "Be careful, that stuff is worth more than you" or "Don't touch the vegetables, they're fragile."