  We calculate the bosonic string one-loop three- and four-point amplitudes to
quadradic order in momentum, and we read off the one-loop low-energy
two-derivative effective action for the massless fields, $S_{eff}$. Treating
the renormalized one-loop vacuum energy as a tunable parameter and
extrapolating to a supercritical dimension $D > 26$, one can reach a regime
where the one-loop couplings in Seff are of the same order as the tree-level
ones while all higher-loop corrections are negligible. Moreover the effective
spacetime curvature is small in string units. We show that the effective action
thus obtained admits weakly-curved de Sitter solutions with constant dilaton at
small string coupling.
