Let $X$ be a smooth, separated complex algebraic variety. By Hironaka, there exists a compactification $j : X \to \bar{X}$ of $X$ so that $\bar{X} \setminus X$ is a simple normal crossings divisor.

Is there some example of a variety $X$ where you cannot choose the compactification such that $\bar{X} \setminus X$ is smooth?