We have used the 2- year Differential Microwave Radiometer data from the COsmic Background Explorer ( COBE ) satellite to systematically search for millimetric ( 31 - 90 GHz ) emission from the Gamma Ray Bursts ( GRBs ) in the Burst And Transient Source Experiment ( BATSE ) GRB 3B catalog . The large beamsize of the COBE instrument ( 7 ^ { \circ } FWHM ) allows for an efficient search of the large GRB positional error boxes , although it also means that fluxes from ( point source ) GRB objects will be somewhat diluted . A likelihood analysis has been used to look for a change in the level of millimetric emission from the locations of 81 GRB events during the first two years ( 1990 & 1991 ) of the COBE mission . The likelihood analysis determined that we did not find any significant millimetric signal before or after the occurance of the GRB . We find 95 % confidence level upper limits of 175 , 192 and 645 Jy or , in terms of fluxes , of 9.6 , 16.3 and 54.8 \cdot 10 ^ { -13 } erg/cm ^ { 2 } s , respectively at 31 , 53 and 90 GHz . We also look separately at different classes of GRBs , including a study of the top ten ( in peak flux ) GRBs , the “ short burst ” and “ long burst ” subsets , finding similar upper limits . While these limits may be somewhat higher than one would like , we estimate that using this technique with future planned missions could push these limits down to \sim 1 mJy .