  In this article, we are interested in metric spaces that satisfy a weak
non-positive curvature condition in the sense that they admit a conical
geodesic bicombing. We show that the analog of a question of Gromov about
compactness properties of convex hulls has a negative answer in this setting.
Specifically, we prove that there exists a complete metric space $X$ that
admits a conical bicombing $\sigma$ such that $X$ has a finite subset whose
closed $\sigma$-convex hull is not compact.
