I hope that this is possible, since I don't have the option of pulling new wire to this location. I want to add a receptacle next to an existing 3-way switch that controls a fluorescent light in a kitchen. Coming into the junction box is a single 12/3 nm cable, with a black, a red, and a white wire (no ground, the installation is probably about 40 years old).

rrpous

If you only have 3 wires at the switch and there all connected to switch, unfortunately
You won't be able to wire in a receptacle as it needs a neutral wire to operate. The device that the switch runs is getting neutral from another location. Probably at the other switch.

As mentiond above, it needs a Neutral. You could Install a wireless X10 3 way switch and a receptacle with existing wiring.