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We present the results of a search in the Galactic plane for $^{56}$Co decay lines at 847 keV and 1238 keV which might have been produced in a previously undetected Galactic supernova. The search is conducted using the continuous data stream from BATSE aboard CGRO and covers a 1037-day interval from 3 June 1991 to 4 April 1994. Our results give upper limit fluxes which are dominated by systematic error, yet are sensitive enough to detect a Type II supernova at 16 kpc or a Type Ia supernova at 1.6 Mpc within a 99\% confidence interval assuming a normal error distribution.
