Based on cosmological rates, it is probable that at least once in the last Gy the Earth has been irradiated by a gamma-ray burst in our Galaxy from within 2 kpc. Using a two-dimensional atmospheric model we have performed the first computation of the effects upon the Earths atmosphere of one such impulsive event. A ten second burst delivering 100 kJ/m^2 to the Earth penetrates to the stratosphere and results in globally averaged ozone depletion of 35%, with depletion reaching 55% at some latitudes. Significant global depletion persists for over 5 years after the burst. This depletion would have dramatic implications for life since a 50% decrease in ozone column density results in approximately three times the normal UVB flux. Widespread extinctions are likely, based on extrapolation from UVB sensitivity of modern organisms. Additional effects include a shot of nitrate fertilizer and NO2 opacity in the visible providing a cooling perturbation to the climate over a similar timescale. These results lend support to the hypothesis that a GRB may have initiated the late Ordovician mass extinction (Melott et al. 2004).