what Alex said is right but in addition(as usual!) it depends on the meaning. chi is informal form of che but sometimes you can't replace che by chi for example: what a beautiful cat: che gorbehye khoshgeli! NOT chi gorbeye khoshgeli cause it's wrong! I love her no matter if she loves me or not: man oo ra doost daram che oo man ra doost dashteh bashad che na. in this case you can't do it again!( in Persian when we use che before two opposite sentence in a conditional phrase it means: anyway ... even if ... or ...) it was two examples in which you learnt we sometimes we can not use chi instead of che. if I remember something else I'll let you know.

as a formal writing or conversation we can't use "chi" because it's wrong. you should use "che". sometimes when you don't understand something in conversation you can use it(chi?= what?) and it's very usual between persian people.

hello... to be honest I didn't get your question ^____^ generally "chi" is a modern form ( in some usages ) and informal form ( in some other usages) of "che". formal usage: "chi" is an interjection like "what?" informal usage: all other usages of "what" should come with "che" and using of "chi" is informal in these cases.