We report N-body simulations of the birthrate and distribution of supernovae in spiral galaxies. The simulations assume that stars form in GMCs with mass greater than 105M⊙ and that a Miller-Scalo IMF results. We assume that the resulting supernovae disrupt the GMC into smaller clouds; these clouds aggregrate to form new GMCs via inelastic collisions. Imposing a spiral potential, we find that supernovae form throughout the disk, but concentrated in the spiral arms. Using conditions appropriate for the Galaxy, a set of simulations with different initial random distributions of molecular clouds predicts 755τ5 supernova remnants (SNR) should exist in the Galaxy (where τ5 is the ratio of the lifetimes of SNRs to 105 yr). The predicted number of remnants and their spatial distribution can be compared to observations.