We study the special algebraic properties of alternating $3$-forms in $6$ dimensions and introduce a diffeomorphism-invariant functional on the space of differential $3$-forms on a closed $6$-manifold $M$. Restricting the functional to a de Rham cohomology class in $H^3(M,\R)$, we find that a critical point which is generic in a suitable sense defines a complex threefold with trivial canonical bundle. This approach gives a direct method of showing that an open set in $H^3(M,\R)$ is a local moduli space for this structure and introduces in a natural way the special pseudo-K\"ahler structure on it.