  We investigate theoretically the ordering effect of quantum spin fluctuations
in a Heisenberg antiferromagnet on a two-dimensional network of corner sharing
tetrahedra. This network is obtained as a {111} slice of the highly frustrated
pyrochlore lattice, from which it inherits the equivalence of all three pairs
of opposite bonds of each tetrahedron. The lowest-order (in 1/S) quantum
corrections partially lift the huge degeneracy of the classical ground state
and select an ensemble of states with long-range valence-bond order.
