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Quasi-periodic solutions of the Gross-Pitaevskii equation with a periodicpotential in dimension three are studied. It is proven that there is anextensive "non-resonant" set ${\mathcal G} \subset \mathbb{R}^3$ such that forevery $\vec k\in \mathcal G$ there is a solution asymptotically close to aplane wave $Ae^{i\langle{ \vec{k}, \vec{x} }\rangle}$ as $|\vec k|\to \infty $,given $A$ is sufficiently small.

Solutions of Gross-Pitaevskii Equation with Periodic Potential in Dimension Three