Chen's conjecture on rationally convex hypersurfaces in $rr^4$

Let $Y\subset \mathbb{R}^4$ be a hypersurface with first Betti number $b_1(Y)=0$, and let $W$ be the domain bounded by $Y$. The domain $W$ is rationally convex if it satisfies the complex-analytic condition of rational convexity. Chen's conjecture. If $W$ is rationally convex, then $Y$ is diffeomorphic to $S^3$. This conjecture concerns the topology of contact type hypersurfaces in the four-dimensional local symplectic setting; the supplied source attributes it to Weimin Chen, but gives no resolution status.