In recent years, Answer Set Programming has gained popularity as a viable paradigm for applications in knowledge representation and reasoning. This paper presents a novel methodology to compute answer sets of an answer set program. The proposed methodology maintains a bottom-up approach to the computation of answer sets (as in existing systems), but it makes use of a novel structuring of the computation, that originates from the non-ground version of the program. Grounding is lazily performed during the computation of the answer sets. The implementation has been realized using Constraint Logic Programming over finite domains.