  The coupled cluster method (CCM) is applied to the spin-one anisotropic
Heisenberg antiferromagnet (HAF) on the square lattice at zero temperature
using a new high-order CCM ground-state formalism for general quantum spin
number ($s \ge 1/2$). The results presented constitute the first such
application of this new formalism, and they are shown to be among the most
accurate results for the ground-state energy and sublattice magnetisation of
this model as yet determined. We ``track'' the solution to the CCM equations at
a given level of approximation with respect to the anisotropy parameter,
$\Delta$, from the trivial Ising limit ($\Delta \to \infty$) down to a critical
value $\Delta_c$, at which point this solution terminates. This behaviour is
associated with a phase transition in the system, and hence a primary result of
these high-order CCM calculations is that they provide an accurate and unbiased
(i.e., {\it ab initio}) estimation of the position of the quantum phase
transition point as a function of the anisotropy parameter. Our result is,
namely, that this point occurs at (or slightly below) the isotropic Heisenberg
point at $\Delta=1$, for this model.
