A search for nu_mu -> nu_e oscillations has been conducted at the Los Alamos Meson Physics Facility using nu_mu from pi^+ decay in flight. An excess in the number of beam-related events from the C(nu_e,e^-)X inclusive reaction is observed. The excess is too large to be explained by normal nu_e contamination in the beam at a confidence level greater than 99%. If interpreted as an oscillation signal, the observed oscillation probability of (2.6 +- 1.0 +- 0.5) x 10^{-3} is consistent with the previously reported nu_mu_bar -> nu_e_bar oscillation evidence from LSND.