A space $X$ (by which I mean a CW complex) is **acyclic** if its reduced singular homology $\tilde H_\ast(X;\Bbb Z)$ is trivial in all degrees.

A discrete group $\pi$ is said to be acyclic if its classifying space $B\pi$ is acyclic.

A space $X$ is **aspherical** if its universal cover is contractible. A space $X$ is **non-aspherical** if its universal cover isn't contractible.

**Question:** Does there exist a *non*-aspherical, acyclic space $X$ whose fundamental group $\pi$ is also acyclic?