Despite a huge number of algorithms and articles published on robsustness issues relating to the convex hull of a finite number of points in n-dimensional Euclidean space, the question of computability of the convex hull, important as it is, has never been addressed in the literature. In this paper, we use the domain-theoretic computable solid modeling framework to show that the convex hull of a finite number of computable points in n-dimensional Euclidean space is indeed computable.