We describe a method for finding flux vacua of type IIB string theory in which the Gukov-Vafa-Witten superpotential is exponentially small. We present an example with $W_0 approx 2 times 10^{-8}$ on an orientifold of a Calabi-Yau hypersurface with $(h^{1,1},h^{2,1})=(2,272)$, at large complex structure and weak string coupling.
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