  We compute the leading corrections to the properties of W and Z bosons
induced at the one-loop level in the SU(5)/SO(5) Littlest Higgs model with T
parity, and perform a global fit to precision electroweak data to determine the
constraints on the model parameters. We find that a large part of the model
parameter space is consistent with data. Values of the symmetry breaking scale
as low as 500 GeV are allowed, indicating that no significant fine tuning in
the Higgs potential is required. We identify a region within the allowed
parameter space in which the lightest T-odd particle, the partner of the
hypercharge gauge boson, has the correct relic abundance to play the role of
dark matter. In addition, we find that a consistent fit to data can be obtained
for large values of the Higgs mass, up to 800 GeV, due to the possibility of a
partial cancellation between the contributions to the T parameter from Higgs
loops and new physics.
