We present Chandra gas temperature profiles at large radii for a sample of 13 nearby, relaxed galaxy clusters and groups, which includes A133, A262, A383, A478, A907, A1413, A1795, A1991, A2029, A2390, MKW4, RXJ1159+5531, and USGC S152. The sample covers a range of average temperatures from 1 to 10 keV. The clusters are selected from the archive or observed by us to have sufficient exposures and off-center area coverage to enable accurate background subtraction and reach the temperature accuracy of better than 20-30% at least to r=0.4-0.5 r_180, and for the three best clusters, to 0.6-0.7 r_180. For all clusters, we find cool gas in the cores, outside of which the temperature reaches a peak at r =~ 0.15 r_180 and then declines to ~0.5 of its peak value at r =~ 0.5 r_180. When the profiles are scaled by the cluster average temperature (excluding cool cores) and the estimated virial radius, they show large scatter at small radii, but remarkable similarity at r>0.1-0.2 r_180 for all but one cluster (A2390). Our results are in good agreement with previous measurements from ASCA by Markevitch et al. and from Beppo-SAX by DeGrandi & Molendi. Four clusters have recent XMM-Newton temperature profiles, two of which agree with our results, and we discuss reasons for disagreement for the other two. The overall shape of temperature profiles at large radii is reproduced in recent cosmological simulations.