Don't get your shorts in a twist just yet. Assuming you're holding it with your drill chuck - there is probably nothing really wrong. Most drill chucks aren't going to hold a reamer with much precision. The length of the reamer will just exacerbate the visible runout - but I disagree with cutting it short. The reason it is long is so it can flex to follow your hole and to absorb runout. Cut it in half and it will have half the runout, but it will be many times more stiff and cut oversize. Try chucking it up a few times, tightening it from different holes in the chuck and follow Gusval's suggestion about tapping the high spots, especially before it is completely tight. This is a good application for your indicator. You will want less than .005" TIR before you cut with it. I aim for under .001"
BTW, reamers like low RPM, moderately high feed in, and the same feed rate back out. Good application for oil too.