Using Lyman-a spectroscopy we observe photoassociation of spin-polarized hydrogen atoms to bound vibrational levels of the triplet a3Sg+potential. At a density of 1016 atoms/cm 3 we directly observe light absorption and fluorescence in the photoassociation process. The observed line positions agree with ab initio calculations to within the precision of present theory. Magnetic sublevels in the photoassociation spectra indicate an effective internal field which we identify with a nonadiabatic term in the Hamiltonian. We present quantitative models for the magnetic field dependence of the molecular energy and the photoassociation line shape.