Recently much attention has been directed to extending logic programming with description logic (DL) expressions, so that logic pro- grams have access to DL knowledge bases and thus are able to reason with ontologies in the Semantic Web. In this paper, we propose a new extension of logic programs with DL expressions, called normal DL logic programs. In a normal DL logic program arbitrary DL expressions are allowed to appear in rule bodies and atomic DL expressions (i.e., atomic concepts and atomic roles) allowed in rule heads. We extend the key condition of well-supportedness for normal logic programs under the standard answer set semantics to normal DL logic programs and define an answer set semantics for DL logic programs which satises the extended well-supportedness condition. We show that the answer set semantics for normal DL logic programs is decidable if the underlying description logic is decidable (e.g. SHOIN or SROIQ).