  We report on the result of an extensive search for X-ray counterparts to
Gamma Ray Bursts (GRB) using data acquired with the Imaging Proportional
Counter (IPC) on-board the Einstein Observatory. We examine background sky
fields from all pointed observations for short timescale (~10 sec) transient
X-ray phenomena not associated a-priori with detectable point sources. A total
of 1.5 X 10^7 seconds of exposure time was searched on arc-minute spatial
scales down to a limiting sensitivity of 10^-11 erg/cm^2/sec in the 0.2-3.5 keV
IPC band. Forty-two highly significant X-ray flashes (Poisson probability <
10^-7 of being produced by statistical fluctuations) are discovered, of which
eighteen have spectra consistent with an extragalactic origin and lightcurves
similar to the Ginga-detected X-ray counterparts to GRB. Great care is taken to
identify and exclude instrumental and observational artifacts; we develop a set
of tests to cull events which may be associated with spacecraft or near-Earth
space backgrounds. The flashes are found to be distributed isotropically on the
sky and have an approximately Euclidean number-size relation. They are not
associated with any known sources and, in particular, they do not correlate
with the nearby galaxy distribution. Whether or not these flashes are
astrophysical and/or associated with GRB, the limits imposed by the search
described herein produces important constraints on GRB models. In this paper,
we discuss possible origins for these flashes; in a companion paper, Hamilton,
Gotthelf, and Helfand (1996) we use the results of our search to constrain
strongly all halo models for GRB.
