Anton Šťastný played his International Hockey for Czechoslovakia, as Slovakia was controlled by Czechoslovakia and considered one it's territories at the time.

Anton Šťastný was the first player born and trained in Slovakia (Bratislava) to be drafted by an NHL team.
Šťastný was originally drafted 198th overall by the Philadelphia Flyers in the 1978 NHL Amateur Draft, but the selection was ruled invalid after it was determined Šťastný was too young to be drafted. He re-entered and was drafted 83rd overall by the Quebec Nordiques in the 1979 NHL Entry Draft.

He played 650 regular season NHL games for the Nordiques, scoring 252 goals and 384 assists. 66 Playoff games, scoring 20 goals and 32 assists.