  Could a conformal Galileon be describing a gauge mode of a broader
diffeomorphism invariant theory? We answer this question affirmatively in 3D by
using a coset construction for a nonlinearly realized conformal symmetry. In
particular, we show that the conformal Galileon emerges as a St\"uckelberg
field of a local Weyl symmetry. The coset construction gives us a
diffeomorphism and Weyl invariant 3D theory containing first, second, and third
powers of the curvatures, their couplings to certain tensors made of the
Galileon and its derivatives, and the conformal Galileon terms. In a theory
with a boundary additional surface terms are required for the boundary Weyl
anomaly cancellation. When gravity is switched off, the theory reduces to the
conformal Galileon plus a boundary term. On the other hand, it reduces to a
generalization of "New Massive Gravity" by A. Sinha, if the Weyl symmetry is
gauge-fixed in a particular way. Last but not least, there exists a parameter
space for which the theory has no propagating ghosts. Thus we show by an
explicit construction that "New Massive Gravity" (and its generalization) is a
unique scalar ghost free low energy effective field theory non-linearly
realizing conformal symmetry in 3D.
