We present V, V-I color-magnitude diagrams (CMDs) for three old star clusters in the Large Magellanic Cloud (LMC): NGC 1466, NGC 2257, and Hodge 11. Our data extend {~}3 mag below the main-sequence turnoff, allowing us to determine accurate relative ages and the blue straggler frequencies. Based on a differential comparison of the CMDs, any age difference between the three LMC clusters is less than 1.5 Gyr. Comparing their CMDs to those of M92 and M3, the LMC clusters, unless their published metallicities are significantly in error, are the same age as the old Galactic globulars. The similar ages to Galactic globulars are shown to be consistent with hierarchical clustering models of galaxy formation. The blue straggler frequencies are also similar to those of Galactic globular clusters. We derive a true distance modulus to the LMC of (m - M)0 = 18.46 {+/-} 0.09 [assuming (m - M)0 = 14.61 for M92] using these three LMC clusters.