We report the first detection of doubly-deuterated methanol (CHD2OH), as well as firm detections of the two singly-deuterated isotopomers of methanol (CH2DOH and CH3OD), towards the solar-type protostar IRAS 16293-2422. From the present multifrequency observations, we derive the following abundance ratios: [CHD2OH]/[CH3OH] = 0.2 +/- 0.1, [CH2DOH]/[CH3OH] = 0.9 +/- 0.3, [CH3OD]/[CH3OH] = 0.04 +/- 0.02. The total abundance of the deuterated forms of methanol is greater than that of its normal hydrogenated counterpart in the circumstellar material of IRAS 16293-2422, a circumstance not previously encountered. Formaldehyde, which is thought to be the chemical precursor of methanol, possesses a much lower fraction of deuterated isotopomers ( ~ 20%) with respect to the main isotopic form in IRAS 16293-2422. The observed fractionation of methanol and formaldehyde provides a severe challenge to both gas-phase and grain-surface models of deuteration. Two examples of the latter model are roughly in agreement with our observations of CHD2OH and CH2DOH if the accreting gas has a large (0.2-0.3) atomic D/H ratio. However, no gas-phase model predicts such a high atomic D/H ratio, and hence some key ingredient seems to be missing.