  In a recent paper, we introduced a new Little Higgs model, which contains the
gauge structure $SU(2)^3\times U(1)$, embedded in an approximate global
$SO(5)\times SO(5)$ symmetry. After breaking to the standard model, $SU(2)_L
\times U(1)_Y$, this produces two heavy $Z^\prime$ bosons and two heavy
$W^{\prime\pm}$ bosons, along with a single Standard Model-like Higgs scalar.
The unique feature of the model was that it was possible to obtain electroweak
symmetry breaking and a light Higgs mass entirely from perturbative loop
contributions to the Higgs effective potential. In this paper we consider the
electroweak constraints on this model, including tree and loop contributions to
the universal oblique and non-oblique parameters, tree-level corrections to the
$ZWW$ vertex, and tree and loop level corrections to $Zb\bar{b}$. The most
significant corrections are positive tree-level corrections to $\hat{S}$ and
negative fermion-loop corrections to $\hat{T}$, which require that the scale
for the global symmetry breaking be $\gtrsim2$ TeV, depending on the top-quark
mixing parameter and the extra gauge couplings. In addition, the loop
corrections to $Zb\bar{b}$ contain a divergence that must be absorbed into the
coefficient of a new operator in the theory. The finite part of this
$Zb\bar{b}$ correction, however, is negligible.
