RhC molecules produced by the vaporization of a mixture of Rh and C powder from a graphite cell have been trapped in the 2Σ+ ground state in neon and argon matrices at 4°K. ESR spectra exhibit hyperfine structure arising from the electron interaction with the 103Rh (100% natural abundance) and 13C (by isotopic enrichment) nuclei, yielding the following parameters in a neon matrix: A∥(Rh)=1113(1) MHz, A⊥ (Rh)=1089(1) MHz, A∥ (C)=89(1) MHz, A⊥ (C)=55(1) MHz, g∥ =2.0039(6) and g⊥ =2.0541(6). The ground state configuration is determined to be largely ··· (4dσ)2 (4dπ)4 (4dδ)4 (5sσ) with some mixing of 4dσ with 5sσ. The relatively large positive value of Δ g⊥ is in agreement with the spin-doubling constant, γ =−0.062, determined earlier in the gas phase and indicates that there is strong coupling between the ground state and an unknown 2Πi state, possibly observed in the ultraviolet in the matrix spectra. Spectra of Rh atoms in a neon matrix observed between 2295 and 3540 Å are compared with known gas-phase transitions.