We have measured the resistance versus magnetic field and Fermi energy for two stadium-shaped cavities in which chaotic scattering is expected. We fit the power spectra of the magnetoresistance fluctuations to semiclassical chaotic scattering theory and find a characteristic field which scales with cavity dimensions as predicted by classical simulations. Measurements of conductance versus Fermi energy indicate a significant contribution from short, non-chaotic paths. We have also studied the energy-averaged conductance as a function of magnetic field. We observe a ballistic weak localization effect similar to that predicted by recent calculations.