  It is shown how to adapt the non-perturbative coupled cluster method of
many-body theory so that it may be successfully applied to Hamiltonian lattice
$SU(N)$ gauge theories. The procedure involves first writing the wavefunctions
for the vacuum and excited states in terms of linked clusters of gauge
invariant excitations of the strong coupling vacuum. The fundamental
approximation scheme then consists of i) a truncation of the infinite set of
clusters in the wavefunctions according to their geometric {\em size}, with all
larger clusters appearing in the Schr\"odinger equations simply discarded, ii)
an expansion of the truncated wavefunctions in terms of the remaining clusters
rearranged, or ``shifted'', to describe gauge invariant {\em fluctuations}
about their vacuum expectation values. The resulting non-linear truncated
Schr\"odinger equations are then solved self-consistently and exactly. Results
are presented for the case of $SU(2)$ in $d=3$ space-time dimensions.
