The BCO molecule, prepared by the reaction of boron atoms with CO, has been trapped in solid neon and argon matrices at 4 K. The X-band electron spin resonance (ESR) spectra in the two matrices were analyzed to show that its ground electronic state is 4-SIGMA, with a zero-field-splitting parameter D = 0.074 cm-1. Hyperfine splittings observed for the B-10, B-11 and C-13 nuclei indicate that the three spins are predominantly on the boron atom. Ab initio calculations, at both the SCF and MBPT(2) levels, find the lowest state of both BCO and BOC to be 4-SIGMA+, but the carbonyl is about 70 kcal/mol more stable than BOC. The calculated spin density on boron in BCO is 0.81 au compared to the experimental value of approximately 0.83 au. Also, calculated harmonic vibrational frequencies for the two molecules are quite different, and the distinctive C-O stretching frequency calculated to lie at 2101 cm-1 for BCO was observed in an argon matrix at 2091 cm-1. The resultant picture of bonding in BCO is almost that of a classic Lewis acid-base bonded complex with the three spins distributed in essentially P-pi-2 and sp-sigma orbitals on boron.