Is topologically massive gravity renormalisable?

Topologically massive gravity is shown to be the unique local dynamical and unitary gravity model which is naive power counting renormalisable. This ultraviolet behaviour is established by an unusual parametrisation of the metric. However, neither covariant nor dimensional regularisation can be implemented. BRST regularisation reveals the possibility of an anomaly term: although it is absent at 1-loop order, where everything is finite, it would require higher-loop calculation to rule it out in general. The viability of this theory is therefore still unclear.