We present a CO (J = 1 --> 0) map of the inner disk of the giant spiral galaxy M101, based on 164 spectra obtained with the NRAO 12 m telescope. A molecular bar 2' in length is detected in the center of M101, a galaxy not previously known to exhibit a bar at any wavelength. R band images reveal a moderate oval distortion in the stellar distribution, which is offset by approximately 25-degrees from the CO bar. Such an offset in position angle between the gaseous and stellar bars is predicted in models by a stellar bar which rotates slowly, such that the corotation radius is significantly beyond the end of the bar. A weak two-arm CO spiral originates from the ends of the CO bar and connects with some of the spiral features seen in the optical. The CO spiral pattern is more symmetric than the optical spiral pattern in the inner galaxy, indicating that the gas has responded more strongly than the stars to the nonaxisymmetric mass distribution. The azimuthally averaged radial distribution of CO emission is well fitted by a single exponential and is similar to the radial distribution of light from old stars but is significantly different from the radial distributions of H-alpha and far-infrared emission, which exhibit a relative excess of emission at intermediate radii. This excess emission is due predominantly to a few extremely luminous H II regions. Either these giant H II regions have an IMF which is enriched in massive stars, or the gas consumption rate is significantly enhanced near these H II complexes. We speculate that some of this behavior is due to a recent infall of intergalactic gas, as evidenced by the high-velocity H I gas detected by van der Hulst and Sancisi.