We report extensive spectroscopic and differential photometric BVRI observations of the active, detached, 1.309-day double-lined eclipsing binary IM Vir, composed of a G7-type primary and a K7 secondary. With these observations, we derive accurate absolute masses and radii of M1=0.981+/-0.012M_{sun}_, M2=0.6644+/-0.0048M_{sun}_, R1=1.061+/-0.016R_{sun}_, and R2=0.681+/-0.013R_{sun}_ for the primary and secondary, with relative errors under 2%. The effective temperatures are 5570+/-100K and 4250+/-130K, respectively. The significant difference in mass makes this a favorable case for comparison with stellar evolution theory. We find that both stars are larger than the models predict, by 3.7% for the primary and 7.5% for the secondary, as well as cooler than expected, by 100K and 150K, respectively. These discrepancies are in line with previously reported differences in low-mass stars, and are believed to be caused by chromospheric activity, which is not accounted for in current models. The effect is not confined to low-mass stars: the rapidly rotating primary of IM Vir joins the growing list of objects of near-solar mass (but still with convective envelopes) that show similar anomalies. The comparison with the models suggests an age of 2.4Gyr for the system, and a metallicity of [Fe/H]~-0.3 that is consistent with other indications, but requires confirmation.