To champion something is to talk highly of it and defend it against attack. A common usage is "to champion a cause", but you could also champion an idea, champion a person, and so on.

.... and just to make the difference clear with regard to the sound of what you heard and what you thought you heard: Presuming the speaker had a non-rhotic accent, the difference between 'cause' and 'course' is only the last consonant. 'Cause' has a voiced consonant /z/, while 'cause' has an unvoiced /s/. In rhotic accents - such as American/Canadian or Scots - the 'r' would make the vowels different, but in British RP, for example, only the /z/ or /s/ at the end would enable you to distinguish between 'course' and 'cause'.

I agree with Richard. What you probably heard was 'champion a cause', which means to support, defend or fight for a cause ( a belief, goal, or ideal).