I think he will run into his <u>ex-girlfriend, but </u>he won't care.
Explanation:
The given sentence is a compound sentence, as it consists of two independent clauses:
I think he will run into his ex-girlfriend.
He won't care.
These sentences are connected by the coordinating conjunction <em>but</em>. Coordinating conjunctions that connect two independent clauses are always preceded by a comma, and that's why there should be a comma between the words <em>ex-girlfriend</em> and <em>but</em>.