  We derive the first law of black hole mechanics in the context of the
Heterotic Superstring effective action to first order in alpha prime using
Wald's formalism. We carefully take into account all the symmetries of the
theory and, as a result, we obtain a manifestly gauge- and Lorentz-invariant
entropy formula in which all the terms can be computed explicitly. An entropy
formula with these properties allows unambiguous calculations of macroscopic
black-hole entropies to first order in alpha prime that can be reliably used in
a comparison with the microscopic ones. Such a formula was still lacking in the
literature. In the proof we use momentum maps to define covariant variations
and Lie derivatives and \textit{restricted generalized zeroth laws} which state
the closedness of certain differential forms on the bifurcation sphere and
imply the constancy of the associated potentials on it. We study the relation
between our entropy formula and other formulae that have been used in the
literature.
