  The chiral boson actions of Floreanini and Jackiw (FJ), and of McClain,Wu and
Yu (MWY) have been recently shown to be different representations of the same
chiral boson theory. MWY displays manifest covariance and also a (gauge)
symmetry that is hidden in the FJ side, which, on the other hand, displays the
physical spectrum in a simple manner. We make use of the covariance of the MWY
representation for the chiral boson to couple it to background gravity showing
explicitly the equivalence with the previous results for the FJ representation
