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Experiments with an external-cavity semiconductor laser indicate that single-frequency oscillation may be obtained in an injection laser when the gain is temporally and spatially stabilized within the active region. Using an originally multimode laser diode as the gain medium, the external-cavity laser oscillates stably in the fundamental spatial mode and in a single longitudinal mode with a frequency which is tunable over a 10 nm spectral range. The rms frequency jitter of the unstabilized laser is 500 kHz. These mode characteristics suggest that spatially inhomogeneous gain saturation is significant only in the lateral direction in the active region of a stripe-geometry double-heterostructure laser diode. A quantitative analysis of the spontaneous emission in the spectral vicinity of the lasing mode shows no evidence of spectral hole burning, with a 0.5 percent upper limit to the depth of the hole burned in the gain spectrum by a lasing mode power of 5 mW.