The yttrium dicarbide molecule, YC2, has been identified in the reactions of laser-ablated yttrium with methane and other small hydrocarbons under supersonic jet-cooled expansion conditions. A parallel-polarized electronic band system with origin at 12889.5 cm(-1) has been tentatively identified as an A(1)-<(X)over tilde (2)A(1)> transition of a "T-shaped" isomer where the Y atom is bonded to the side of a C-2 molecule. Weak vibronically induced perpendicular bands, representing Delta upsilon(3)=odd transitions, are also present. Extensive vibrational progressions in the excitation and the resolved fluorescence spectra have been analyzed to give the two lowest vibrational frequencies of the two electronic states : (X) over tilde (2)A(1), nu(2) (a(1))=561.1(+/-2.8 cm(-1)), nu(3) (b(2))=369.6 (+/-1.7 cm(-1)); excited A(1), nu(2)=494.5(+/-5.0 cm(-1)), nu(3)=331.6(+/-2.2 cm(-1)). No bands involving the C-C stretching vibration (nu(1),a(1)) have been found. The frequency of the vibration in the ground state indicates that the barrier to internal rotation of the C-2 group against the Y atom is quite high, but large anharmonic coupling between the nu(2) and nu(3) vibrations suggests that internal rotation is facilitated by excitation of the Y-C-2 stretohing vibration.