  The a-function is a proposed quantity defined for quantum field theories
which has a monotonic behaviour along renormalisation group flows, being
related to the beta-functions via a gradient flow equation involving a positive
definite metric. We demonstrate the existence of a candidate a-function for
renormalisable Chern-Simons theories in three dimensions, involving scalar and
fermion fields, in both non-supersymmetric and supersymmetric cases.
