From the googly eyes Cho and Harry are making at each other on the train to Hogwarts at the beginning of the film, we are guessing that these two want to become more than friends/fellow students.
However, it's not in the cards for them—at least, not at this point. Harry waits so long to ask Cho to the Yule Ball that she accepts an invite from someone else. She seems pretty disappointed when she realizes that she could have gone with Harry:
HARRY: I was just wondering if maybe you wanted to go to the ball with me.
CHO: Oh, um, Harry, I'm sorry, but someone's already asked me. And. . . .well, I've said I'll go with him.
HARRY: Okay. Yeah. Great. Fine. No problem. Okay. Good.
CHO: Harry? I really am sorry.
Oh, and the whole thing causes some decent tension between Cedric and Harry, when Harry realizes that his fellow Triwizard competitor is Cho's date.
Then, to make things more complicated, Cedric dies in the Triwizard Tournament, and Cho is devastated. It seems that her feelings for him had deepened since the Yule Ball. We're guessing that whole sitch could complicate any future that Charry (which is obviously their celebrity couple name) might have.