We calculate the reaction cross-sections for the fusion of hydrogen and deuterium in strong magnetic fields as are believed to exist in the atmospheres of neutron stars. We find that in the presence of a strong magnetic field ($B \gsim 10^{12}$G), the reaction rates are many orders of magnitude higher than in the unmagnetized case. The fusion of both protons and deuterons are important over a neutron star's lifetime for ultrastrong magnetic fields ($B \sim 10^{16}$G). The enhancement may have dramatic effects on thermonuclear runaways and bursts on the surfaces of neutron stars.

13 pages, 6 figures