  We report ab initio quantum chemical cluster calculations of the chain (J_a)
and the largest interchain (J_b) Heisenberg exchange of the chain cuprates
Ca_2CuO_3 and Sr_2CuO_3. We find that J_a is comparable to the in-plane J in
layered cuprates and J_a/J_b ~250-400. Using recent theory we obtain close
agreement with experiment for the staggered moments and the critical
temperatures. This implies that T_N does not depend on the third parameter J_c
<< J_b, and cannot be calculated using spin-wave theory. We propose an
explanation for this interms of a 1D->2D cross-over.
