  We construct a weakly coupled, renormalizable ultraviolet completion of the
Littlest Higgs model with T-parity (LHT), based on an SU(5)xSU(2)xU(1) gauge
theory with a discrete Z_2 symmetry. Our model reproduces the complete
structure of the LHT below the 10 TeV scale, including the collective symmetry
breaking mechanism which solves the little hierarchy problem. The model is
manifestly free of anomalies, including both gauge/gravitational anomalies and
anomalies involving T-parity. At the TeV scale, the model contains additional
states not present in the LHT. We estimate the impact of these states on
precision electroweak observables, and show that the model is realistic. We
also discuss how our model can be embedded into a supersymmetric theory or a
five-dimensional setup with a warped extra dimension, stabilyzing the hierarchy
between the 10 TeV and the Planck scale.
