Yes, the sentence "The little boy didn't do his homework nor his chores" is a complete sentence. It contains a subject ("The little boy") and a verb phrase ("didn't do") that expresses a complete thought. The words "nor his chores" are coordinating conjunctions that connect two verb phrases ("do his homework" and "do his chores"). To determine whether a sentence is complete or not, you can look for a subject and a verb that express a complete thought.
