We consider hot accretion disk outflows from black hole - neutron star mergers in the context of the nucleosynthesis they produce. We begin with a three dimensional numerical model of a black hole - neutron star merger and calculate the neutrino and antineutrino fluxes emitted from the resulting accretion disk. We then follow the element synthesis in material outflowing the disk along parameterized trajectories. We find that at least a weak r-process is produced, and in some cases a main r-process as well. The neutron-rich conditions required for this production of r-process nuclei stem directly from the interactions of the neutrinos emitted by the disk with the free neutrons and protons in the outflow.