 Billington was selected by the Colorado Avalanche during the waiver draft held on September 30, 1996.On October 17, Billington made his Avalanche debut, making 30 saves in a 2-1 loss to the Florida Panthers.In his next start, on October 28, Billington stopped all 40 shots he faced in a 1-0 victory over the Washington Capitals for his first win with the Avalanche.