Localization based super-resolution microscopy techniques require precise drift correction methods because the achieved spatial resolution is close to both the mechanical and optical performance limits of modern light microscopes. Multi-color imaging methods require corrections in addition to those dealing with drift due to the static, but spatially-dependent, chromatic offset between images. We present computer simulations to quantify this effect, which is primarily caused by the high-NA objectives used in super-resolution microscopy. Although the chromatic offset in well corrected systems is only a fraction of an optical wavelength in magnitude (<50 nm) and thus negligible in traditional diffraction limited imaging, we show that object colocalization by multi-color super-resolution methods is impossible without appropriate image correction. The simulated data are in excellent agreement with experiments using fluorescent beads excited and localized at multiple wavelengths. Finally we present a rigorous and practical calibration protocol to correct for chromatic optical offset, and demonstrate its efficacy for the imaging of transferrin receptor protein colocalization in HeLa cells using two-color direct stochastic optical reconstruction microscopy (dSTORM).