The angular expansion rate of the X-ray remnant of the supernova (SN) observed by Tycho Brahe in AD 1572 has been determined using observations by ROSAT. From two High Resolution Imager (HRI) pointings separated in time by 4.5 yr, I determine a mean expansion rate for the blast wave of yr , which is larger than published results from optical and radio observations. The X-ray expansion is consistent with the dynamical evolution expected from a young ejecta-dominated remnant which has experienced only modest deceleration. I find evidence for differential expansion in that the interior of the remnant appears to be expanding at a somewhat slower rate. The expansion rate varies significantly with azimuth as well. In particular, I find that two small knots in the southeastern part of Tycho are moving more rapidly than any other feature in the X-ray image. Previous work has established that these knots are clumps of highly enriched stellar ejecta with very different abundance distributions. This is the first evidence for ejecta ``bullets'' in the remnant of a Type Ia SN.