From Longman Dictionary of Contemporary Englishfull/packed/stuffed etc to the gillsfull/packed/stuffed etc to the gillsinformal completely full The bar was packed to the gills on Monday. → gill
Examples from the Corpus
full/packed/stuffed etc to the gills• If Tapie was a fish he'd be stuffed to the gills this issue!• It's a surprise then to find the Powerhaus pretty much packed to the gills. 