"Tchip" is a "suck" sound produced by the mouth, saliva and teeth (often accompanied by a skewed look) that is mostly used when you are annoyed. This noise often comes from people of African ethnicity.

when you're hungover as shit after a spending a night drunk as a skunk

From Africa "tchip" is an exclamation (an agressive sucking noise, that you make with your mouth) more often used by Black people for expressed the annoyance and the dissatisfaction. and is also a bad word which mean "shup up", "damn"...Etc