Klt degenerations of projective spaces

We study degenerations of complex projective spaces ${\mathbb{P}}^n$ into normal projective klt varieties $X$. If the tangent sheaf of $X$ is semi-stable, we show that $X$ itself is a projective space. If $X$ is a threefold with canonical singularities, we show that there are only three varieties which satisfy all the conditions.