  The $S=1/2$, nearest-neighbor, quantum Heisenberg antiferromagnet on the
square lattice with spatially anisotropic couplings is reconsidered, with
particular attention to the following question: at T=0, does N\'eel
orderdevelop at infinitesimal interchain coupling, or is there a nonzero
critical coupling? A heuristic renormalization group argument is presented
which suggests that previous theoretical answers to that question are incorrect
or at least incomplete, and that the answer is not universal but rather depends
on the microscopic details of the model under consideration. Numerical
investigations of the nearest-neighbor model are carried out {\it via}
zero-temperature series expansions about Ising and dimer Hamiltonians. The
results are entirely consistent with a vanishing critical interchain coupling
ratio $R_c$; if $R_c$ is finite, it is unlikely to substantially exceed 0.02.
