We present ALMA observations of protoplanetary disks ( “ proplyds ” ) in the Orion Nebula Cluster . We imaged 5 individual fields at 856 \micron containing 22 HST -identified proplyds and detected 21 of them . Eight of those disks were detected for the first time at submillimeter wavelengths , including the most prominent , well-known proplyd in the entire Orion Nebula , 114-426 . Thermal dust emission in excess of any free-free component was measured in all but one of the detected disks , and ranged between 1–163 mJy , with resulting disk masses of 0.3 - 79 M _ { jup } . An additional 26 stars with no prior evidence of associated disks in HST observations were also imaged within the 5 fields , but only 2 were detected . The disk mass upper limits for the undetected targets , which include OB stars , \theta ^ { 1 } Ori C and \theta ^ { 1 } Ori F , range from 0.1–0.6 M _ { jup } . Combining these ALMA data with previous SMA observations , we find a lack of massive ( \gtrsim 3 M _ { jup } ) disks in the extreme-UV dominated region of Orion , within 0.03 pc of \theta ^ { 1 } Ori C. At larger separations from \theta ^ { 1 } Ori C , in the far-UV dominated region , there is a wide range of disk masses , similar to what is found in low-mass star forming regions . Taken together , these results suggest that a rapid dissipation of disk masses likely inhibits potential planet formation in the extreme-UV dominated regions of OB associations , but leaves disks in the far-UV dominated regions relatively unaffected .