We provide an ExpTime algorithm for answering conjunctive queries (CQs) in Horn- SHIQ\mathcal{SHIQ} , a Horn fragment of the well-known Description Logic SHIQ\mathcal{SHIQ} underlying the OWL-Lite standard. The algorithm employs a domino system for model representation, which is constructed via a worst-case optimal tableau algorithm for Horn- SHIQ\mathcal{SHIQ} ; the queries are answered by reasoning over the domino system. Our algorithm not only shows that CQ answering in Horn- SHIQ\mathcal{SHIQ} is not harder than satisfiability testing, but also that it is polynomial in data complexity, making Horn- SHIQ\mathcal{SHIQ} an attractive expressive Description Logic.