  We investigate in which sense, at the linearized level, one can extend the 3D
topologically massive gravity theory beyond three dimensions. We show that, for
each k=1,2,3... a free topologically massive gauge theory in 4k-1 dimensions
can be defined describing a massive "spin-2" particle provided one uses a
non-standard representation of the massive "spin-2" state which makes use of a
two-column Young tableau where each column is of height 2k-1. We work out the
case of k=2, i.e. 7D, and show, by canonical analysis, that the model
describes, unitarily, 35 massive "spin-2" degrees of freedom. The issue of
interactions is discussed and compared with the three-dimensional situation.
