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We have built a low-power CW HF/DF chemical laser, designed to achieve high-frequency stability. Measurements are reported which characterize the instantaneous spectral width of the laser output to less than one part in 1011( kHz) and the variations in absolute frequency of this emission with time to four parts in 1010( kHz) per 0.1 ms. Two experiments to actively stabilize the laser frequency are reported. In one experiment the laser was locked to a high-finesse Fabry-Perot to five parts in 109( kHz) for many minutes. In the other experiment one laser was locked to another using heterodyne beat spectroscopy to 1.7 parts in 109( kHz). The stabilization experiments were limited by the feedback loops used.