Deuterated methanol is one of the most robust windows astrochemists have on the individual chemical reactions forming deuterium-bearing molecules and the physicochemical history of the regions where they reside. The first-time detection of mono- and di-deuterated methanol in a cometary coma is presented for comet 67P/Churyumov-Gerasimenko using Rosetta-ROSINA data. D-methanol (CH_3_OD and CH_2_DOH combined) and D_2_-methanol (CH_2_DOD and CHD_2_OH combined) have an abundance of 5.5+/0.46 and 0.00069+/-0.00014 per cent relative to normal methanol. The data span a methanol deuteration fraction (D/H ratio) in the 0.71-6.6 per cent range, accounting for statistical corrections for the location of D in the molecule and including statistical error propagation in the ROSINA measurements. It is argued that cometary CH_2_DOH forms from CO hydrogenation to CH_3_OH and subsequent H-D substitution reactions in CH_3_-R. CHD_2_OH is likely produced from deuterated formaldehyde. Meanwhile, CH_3_OD and CH_2_DOD could form via H-D exchange reactions in OH-R in the presence of deuterated water ice. Methanol formation and deuteration is argued to occur at the same epoch as D_2_O formation from HDO, with formation of mono-deuterated water, hydrogen sulphide, and ammonia occurring prior to that. The cometary D-methanol/methanol ratio is demonstrated to agree most closely with that in prestellar cores and low-mass protostellar regions. The results suggest that cometary methanol stems from the innate cold (10-20K) prestellar core that birthed our Solar system. Cometary volatiles individually reflect the evolutionary phases of star formation from cloud to core to protostar.