The A2 experiment on HEAO-1 was especially developed to make systematics-free measurements of the extragalactic X-ray background (Boldt et al. 1979) over the band (up to 60 keV) of maximum flux. The spectrum observed has a remarkably simple thermal form (Marshall et al. 1980) with a mean photon energy of about 40 keV, an order of magnitude above the high-energy limit of the Einstein Observatory (HEAO-2) telescope. If most of this hard X-ray flux is not diffuse, then the main sources of this background could be 1) unresolved objects of known classification (e.g. BL Lac type, quasars, active galaxies) at high redshift, 2) redshifted (z > 1) gamma-ray bursts and/or 3) a new class of X-ray objects peculiar to high redshifts. If we assume that the number of such sources that are highly variable is less than 106, then our first-cut analysis of the temporal stability measured for the X-ray background indicates that 1) their contribution is less than 15% if they are variable on scales less than 104 seconds, and 2) their contribution is less than 60% if they are variable on scales less than a half-year.