We present an analysis of the X-ray content of the 1978 November 19 gamma-ray burst error box using ASCA. We confirm the presence of a source that was detected by Einstein, but not confirmed by EXOSAT, and measure its spectrum between 0.5 and 8 keV. Using a power-law fit with an index of 1.77, the source flux is 1.6 X 10-13 erg cm-2 s-1. This source was also observed by ROSAT. Using both old and new optical and radio data, we examine a possible counterpart for the X-ray source. We find that the probability of a chance association between the X-ray source and the gamma-ray burst error box is small enough to warrant its consideration as a possible counterpart to the burst source.
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