  We study the ground state properties of an anisotropic, quasi-2D version of
the quantum (S=1/2) pyrochlore antiferromagnet. In the presence of
Dzyaloshinsky-Moriya interactions, in addition to the Heisenberg exchanges, it
is shown that two types of ordered magnetic states are generally possible: non
coplanar "chiral," and coplanar antiferromagnetic order. The magnetic moments
in all cases are determined by the Dzyaloshinsky-Moriya interactions and in
this sense the antiferromagnetic order is "weak."
