[Nagoyankee]

lol This is something your dictionary won't help you understand. It's all colloquial.

ちょー means 'very', 'extreme(ly)', 'really', etc.

かっこつけ means someone who likes to look cooler than he actually is or the act of trying to look cool.

So, ちょーかっこつけ means "(Someone is) trying really hard to look cool."

(Only the context will tell who that someone can be. )

EDIT: MMM beat me to it.