The cat was placed in a box with a jar of cyanide, that was connected to a timer and geiger counter. The timer was set in such a way that there is a 50-50 chance of the cat dying based on the decay of a radioactive atom. This was a thought experiment which, among other things, demonstrated that there is no clear and definite boundary between quantum causality and macroscopic causality. The reality of quantum processes cannot be relegated to the microscopic world. For instance, Murray Gell-Mann refers to human existence as due to 'accidents' of nature.
Chance is nothing, and therefore can be the cause of nothing.
But I don't think physicists mean to use the term chance this way. They are in thermal motion. They constantly shift their patterns in a very complex way. This complex, changing set of patterns we refer to as 'random'. A particular event selected from among these patterns may arise by 'chance'.