  We follow the example of Tutte in his construction of the dichromate of a
graph (that is, the Tutte polynomial) as a unification of the chromatic
polynomial and the flow polynomial in order to construct a new polynomial
invariant of maps (graphs embedded in orientable surfaces). We call this the
surface Tutte polynomial. The surface Tutte polynomial of a map contains the
Las Vergnas polynomial, Bollob\'as-Riordan polynomial and Kruskhal polynomial
as specializations. By construction, the surface Tutte polynomial includes
among its evaluations the number of local tensions and local flows taking
values in any given finite group. Other evaluations include the number of
quasi-forests.
