Our observation of 1−mm wavelength radiation generated in a cavity containing a Josephson junction provides evidence for a negative effective microwave resistance in the Josephson junction, and for parametric amplification in the reflection mode by the Josephson junction. These parametric oscillations were observed at wavelengths corresponding to cavity resonances between 1.1− and 2−mm wavelength. The frequency of the emitted radiation differed from the frequency given by ν=2eV/h, and thus the radiation was not simply from the ac Josephson effect. We develop a theory that predicts a negative microwave resistance at junction bias voltages just below a cavity−induced step for resistively shunted junction, and just above the cavity−induced step for a junction with sufficient shunt capacitance. Our observations are consistent with the theory.