The negative molecular ion C3N- has been detected at millimeter wavelengths in a low-pressure laboratory discharge, and then with frequencies derived from the laboratory data in the molecular envelope of IRC+10216. Spectroscopic constants derived from laboratory measurements of 12 transitions between 97 and 378 GHz allow the rotational spectrum to be calculated well into the submillimeter-wave band to 0.03 km s-1 or better in equivalent radial velocity. Four transitions of C3N- were detected in IRC+10216 with the IRAM 30 m telescope at precisely the frequencies calculated from the laboratory measurements. The column density of C3N- is 0.5% that of C3N, or approximately 20 times greater than that of C4H- relative to C4H. The C3N- abundance in IRC+10216 is compared with a chemical model calculation by Petrie & Herbst. An upper limit in TMC-1 for C3N- relative to C3N (<0.8%) and a limit for C4H- relative to C4H (<0.004%) that is 5 times lower than that found in IRC+10216, were obtained from observations with the NRAO 100 m Green Bank Telescope (GBT). The fairly high concentration of C3N- achieved in the laboratory implies that other molecular anions containing the CN group may be within reach.