The paper describes the formalization and implementation of an efficient constraint programming framework operating on 3D crystal lattices. The framework is motivated and applied to address the problem of solving the abinitio protein structure prediction problem - i.e., predicting the 3D structure of a protein from its amino acid sequence. Experimental results demonstrate that our novel approach offers up to a 3 orders of magnitude of speedup compared to other constraint-based solutions proposed for the problem at hand.