  We propose a new class of conformal higher spin gravities in three
dimensions, which extends the one by Pope and Townsend. The main new feature is
that there are infinitely many examples of the new theories with a finite
number of higher spin fields, much as in the massless case. The action has the
Chern-Simons form for a higher spin extension of the conformal algebra. In
general, the new theories contain Fradkin-Tseytlin fields with higher
derivatives in the gauge transformations, which is reminiscent of
partially-massless fields. A relation of the old and new theories to the parity
anomaly is pointed out.
