  We show that the new classical action for two dimensional gravity (the
Jackiw-Teitelboim model) possesses a $W_3$ algebra. We quantise the resulting
$W_3$ gravity in the presence of matter fields with arbitrary central charges
and obtain the critical exponents. The auxiliary field of the model, expressing
the constancy of the scalar curvature, can be interpreted as one of the
physical degrees of freedom of the $W_3$ gravity. Our expressions are
corrections to some previously published results for this model where the $W_3$
symmetry was not accounted for.
