Let $\mathcal{X}\rightarrow D$ be a maximally unipotent degeneration of simply-connected Calabi-Yau manifolds with full $SU(n)$ holonomy, $t_{i}\in D$ with $t_{i}\rightarrow 0$, and let $g_{i}$ be a Ricci-flat metric on $\mathcal{X}_{t_{i}}$ normalized to have fixed diameter $C$. Then a convergent subsequence of $(\mathcal{X}_{t_{i}},g_{i})$ converges to a metric space $(X_{\infty},d_{\infty})$, where $X_{\infty}$ is homeomorphic to $S^{n}$. Furthermore, $d_{\infty}$ is induced by a Riemannian metric on $X_{\infty}\setminus\Gamma$, where $\Gamma\subseteq X_{\infty}$ is a set of codimension two.