  We consider 2+1 dimensional compact U(1) gauge theory at the Lifshitz point
with dynamical critical exponent $z=2$. As in the usual $z=1$ theory, monopoles
proliferate the vacuum for any value of the coupling, generating a mass scale.
The theory of the dilute monopole gas is written in terms a non-relativistic
Sine-Gordon model with two real fields. While monopoles remove some of the
massless poles of the perturbative field strength propagator, a gapless mode
representing the incomplete screening of monopoles remains, and is protected by
a shift invariance of the original theory. Timelike Wilson loops still obey
area laws, implying that minimal charges are confined, but the action of
spacelike Wilson loops of linear size L goes instead as $L^3$.
