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Recent ROSAT Position Sensitive Proportional Counter (PSPC) observations for the first time unequivocally reveal the presence of a compact source of hard X-ray emission centered on the peculiar star $\eta$ Carinae. These observations also show a dramatic change in the hard-band ($E \ge$ 1.6 keV) counting rate by $\approx$ a factor of 2 in a 4-month interval. ROSAT High Resolution Imager (HRI) observations which span the PSPC observations also reveal a variable source of X-ray emission centered on $\eta$ Carinae. Thus strong variability which is a characteristic of $\eta$ Carinae in radio through IR and visible-band wavelengths is also observed at X-ray energies. The increase in hard X-ray emission could be the result of a tripling of the mass-loss rate in less than 4 months.