The National Basketball Association hasn't, as far as I know, ever played games on Christmas Eve, but has played games on Christmas Day for most of the league's history. And there has been at least one nationally televised NBA game on Christmas Day every year since 1969 (as fast as I've been able to determine; perhaps there had been nationally televised Christmas Day NBA games prior to 1969).
After doing further research, I discovered that the first nationally televised NBA Christmas Day game was in 1967, when ABC carried a game between the then-San Diego Rockets and the Los Angeles Lakers played in San Diego (the team nickname stemmed from.the fact that the Atlas rocket, a mainstay of both America's national defense and the space program in the 1960's, was built in San Diego. The nickname was kept after the team moved to Houston, since Houston is the administrative headquarters of NASA's manned space program).