The Sub-Millimetre Radiometer (SMR) aboard the Odin satellite has been measuring vertical profiles of atmospheric trace gases since August 2001. We present the inversion methodology developed for CO measurements and the first retrieval results. CO can be retrieved from a single scan measurement throughout the middle atmosphere, with a typical resolution of ~3 km and a relative error of ~10% to ~25%. Retrieval results are evaluated through comparison with data from the Whole Atmosphere Community Climate Model (WACCM) and observations of the Improved Stratospheric and Mesospheric Sounder (ISAMS) on board the Upper Atmospheric Research Satellite (UARS). Considering the large natural variability of CO, the SMR retrievals give good confirmation of the WACCM results, with an overall agreement within a factor of 2. ISAMS abundances are higher than SMR mixing ratios by a factor of 5--10 above 0.5 hPa from ~80¿S to ~50¿N.