The ROSAT PSPC observation of the face-on spiral galaxy M101 shows conclusive evidence for diffuse X-ray emission. While the emission is strongest in the 1/4 keV band (sensitive to thermal emission near 10(6) K), it is also apparent at 3/4 keV (sensitive to thermal emission at a few 10(6) K). The emission is clearly visible over the inner 7' radius (similar to 15 kpc with a distance to M101 of 7.2 Mpc), or roughly 60% of the D-25 radius. In addition to the emission, a thick spiral arm at roughly an 8' radius in the southwest quadrant is correlated with a depression in surface brightness relative to the region of the observation external to the galaxy. The depression is consistent with the absorption of the entire previously observed extragalactic background at 1/4 keV. The observed 1/4 keV band intensity of M101 varies over the inner 7' of the galaxy with an average value of similar to 790 x 10(-6) counts s(-1) arcmin(-2) and is peaked toward the center of the galaxy. The R2/R1 band ratio implies an emission temperature of similar to 10(5.8) K. After correction for absorption by material associated with Milky Way H I, this implies an intensity of similar to 3280 x 10(-6) counts s(-1) arcmin(-2). This emission most likely originates in the halo of M101 (similar to the 1/4 keV emission detected by ROSAT in NGC 253). If so, it would require an average filling factor of similar to 1 of regions similar to the bright 1/4 keV halo emission observed in our own Galaxy in the direction of Draco. The emission is unlikely to originate in confined regions in the disk of M101, similar to the Local Hot Bubble (T similar to 10(6) K, similar to 1.5 x 10(20) cm(-2) overburden of H I), since the required filling factor of such regions would be much greater than unity and the implied emission temperature would be relatively low (similar to 10(5.5) K). Compared to the Milky Way, either intrinsically brighter but cooler regions or a highly clumped interstellar medium (ISM), or both, would be required if the emission originates in the disk. This detection of extensive diffuse X-ray emission from the halo of a galaxy similar to the Milky Way has implications for our own Galaxy, as well as for M101 itself. By analogy, it implies that the X-ray halo that we observe in the Milky Way has a low filling factor outside the Galactic center region. This is consistent with the apparent patchiness in the solar vicinity.