We present a new method, PARsing And visual GrOuNding (ParaGon), for grounding natural language in object placement tasks. Natural language generally describes objects and spatial relations with compositionality and ambiguity, two major obstacles to effective language grounding. For compositionality, ParaGon parses a language instruction into an object-centric graph representation to ground objects individually. For ambiguity, ParaGon uses a novel particle-based graph neural network to reason about object placements with uncertainty. Essentially, ParaGon integrates a parsing algorithm into a probabilistic, data-driven learning framework. It is fully differentiable and trained end-to-end from data for robustness against complex, ambiguous language input.