I frequently hear this.

Problem:
“I could care less” is the opposite of what is meant.

Explanation:
“I could care less” means that it is possible (“could”) for me to care less. This means that I do care at least a little. When people say, “I could care less,” what they want to say is that they have absolutely no care for whatever the target of their statement is. The only way that this is possible is for them not to be able (“couldn’t”) to care less.

I also believe that omission of “not” (or its contracted form) helps to prove my “Devolution toward Simpler” linguistic hypothesis. It is simpler to say “could” than to say “couldn’t”.

Solution:
“I couldn’t care less.”