We propose ordered choice diagrams (OCD) for symbolic representation of boolean functions. An OCD is a nondeterministic variant of an ordered binary decision diagram (BDD) with appropriate reduction rules. The introduction of nondeterminism destroys canonicity, but affords significant succinctness. While OCDs have efficient algorithms for union, intersection, existential quantifier elimination, and emptiness test, the equivalence problems for OCDs is coNP-complete. We show that symbolic model checking can still be performed efficiently by replacing equivalence test with a stronger equality test. We report on a prototype implementation and preliminary results that indicate the advantage of OCD-based representation in reachability analysis of distributed protocols.