  An $L \times \infty$ system of odd number of coupled Heisenberg spin chains
is studied using a degenerate perturbation theory, where $L$ is the number of
coupled chains. An effective chain Hamiltonian is derived explicitly in terms
of two spin half degrees of freedom of a closed chain of $L$ sites, valid in
the regime the inter-chain coupling is stronger than the intra-chain coupling.
The spin gap has been calculated numerically using the effective Hamiltonian
for $L=3,5,7,9$ for a finite chain up to ten sites. It is suggested that the
ground state of the effective Hamiltonian is correlated, by examining
variational states for the effective chiral-spin chain Hamiltonian.
