I have determined the expansion of the supernova remnant of SN 1604 (Kepler's supernova) based on archival Chandra ACIS-S observations made in 2000 and 2006. The measurements were done in several distinct energy bands, and were made for the remnant as a whole, and for six individual sectors. The average expansion parameter indicates that the remnant expands on average as r proportional to t(0.5), but there are significant differences in different parts of the remnant: the bright northwestern part expands as r proportional to t(0.35), whereas the rest of the remnant's expansion shows an expansion r proportional to t(0.6). The latter is consistent with an explosion in which the outer part of the ejecta has a negative power law slope for density (rho proportional to / v(-n)) of n = 7, or with an exponential density profile [ rho proportional to exp( -v/v(e))]. The expansion parameter in the southern region, in conjunction with the shock radius, indicates a rather low value (< 5 x 10(50) erg) for the explosion energy of SN 1604 for a distance of 4 kpc. A higher explosion energy is consistent with the results if the distance is larger. The filament in the eastern part of the remnant, which is dominated by X- ray synchrotron radiation, seems to mark a region with a fast shock speed r proportional to t(0.7), corresponding to a shock velocity of v = 4200 km s(-1), for a distance to SN 1604 of 4 kpc. This is consistent with the idea that X- ray synchrotron emission requires shock velocities in excess of similar to 2000 km s(-1). The X-ray-based expansion measurements reported are consistent with results based on optical and radio measurements but disagree with previous X- ray measurements based on ROSATand Einstein observations.