The nature of the ordering of a quantum spin‐1/2 Heisenberg antiferromagnet is considered in the presence of the strong lattice frustration associated with the pyrochlore lattice. A field theory indicates that quantum fluctuations lead to a state having dimerization that has long‐range static correlations not in 〈S〉 but rather in 〈S(r)⋅S(r+δ)〉. A sublattice ordering is found that is consistent with results obtained using degenerate perturbation theory to analyze the ground‐state manifold.