In the (Northeastern) United States, I've never heard the word "chum" used as a term of endearment outside of old (or period) films; it may be more common other certain areas and social circles. Chump, I would say, is equally rare. Both terms are rather dated.
However, I would argue that the frequency doesn't particularly matter, because the phrase "Hey, chump!" would be easily identified by the subsequent obnoxious comments, threats, or otherwise inflammatory remarks.
For the most part, those words aren't used anymore – I have seen, however, an increasing use of the word "champ" (as in, a shortened form of "champion") as both a term of endearment and as a sarcastic, often-patronizing insult (with varying degrees of severity; sometimes it's completely mean-spirited, and sometimes it's just some casual, friendly ribbing, as in, "Nice job, champ."). Unfortunately, if you're hearing that one, it's not necessarily going to be easy to tell how it is intended. You'll have to pick up on contextual clues and body language.
I have no idea how much of an isolated term "champ", in that context, is. Has anyone else heard it?