The unstable star η Carinae is arguably the Galaxy's most massive known star or an extremely peculiar massive binary. We report first results of ∼ weekly RXTE monitoring of η Car during the 1996 Feb - 1997 Jun interval, with daily coverage in 1997 Jun-Jul; this represents the most detailed description of the X-ray emission of this or any other massive star. Our RXTE results show a progressive increase in the average 2-10 keV flux through the observing interval. Most surprisingly, we find peaks in the X-ray lightcurve which occur every 85±1.2 days. We consider possible causes of the X-ray variations.