  We evaluate the vacuum expectation value of the central charge operator in
string theory in an AdS3 vacuum. Our calculation provides a rare non-zero
one-point function on a spherical worldsheet. The evaluation involves the
regularization both of a worldsheet ultraviolet divergence (associated to the
infinite volume of the conformal Killing group), and a space-time infrared
divergence (corresponding to the infinite volume of space-time). The two
divergences conspire to give a finite result, which is the classical general
relativity value for the central charge, corrected in bosonic string theory by
an infinite series of tree level higher derivative terms.
