We report precision atmospheric spectroscopy of CO₂ using a laser heterodyne radiometer (LHR) calibrated with an optical frequency comb. Using the comb calibrated LHR, we record spectra of atmospheric CO₂ near 1572.33 nm with a spectral resolution of 200 MHz, using sunlight as a light source. The measured CO₂ spectra exhibit frequency shifts by approximately 11 MHz over the course of the 5-h measurement, and we show that these shifts are caused by Doppler effects due to wind along the spectrometer line of sight. The measured frequency shifts are in excellent agreement with an atmospheric model, and we show that our measurements track the wind-induced Doppler shifts with a relative frequency precision of 2 MHz (3 m·s⁻¹) for a single 10 s measurement, improving to 100 kHz (15 cm·s⁻¹) after averaging (equivalent to a fractional precision of a few parts in 10¹⁰). These results demonstrate that frequency comb calibrated LHR enables precision velocimetry that can be of use in applications ranging from climate science to astronomy.