Let $X$ be a CAT(0) space and $G$ its group of isometries. Then $X$ is said to be cocompact, if there exists a compact set $K\subset X$ with $X=G.K$. The space $X$ is called periodic, if there exists a locally isometric covering $X\to C$ where $C$ is a compact metric space. If $X$ is periodic, then $X$ is the universal covering of $C$ and the group of deck transformations is included in $G$, so $X$ is cocompact.

My question is for the converse: If $X$ is cocompact, is it true that $X$ is periodic? This means, is it true that there exists a subgroup $\Gamma$ of $G$ which acts properly discontinuously such that the quotient $\Gamma\backslash X$ is compact?

If this is not true for general CAT(0) spaces, what if $X$ is a building?