We show that a CR function of class $C^k$, 0 ≤ k < ∞, on a tube submanifold of ${ℂ}^n$ holomorphically extends to the convex hull of the submanifold. The extension and all its derivatives through order k are shown to have nontangential pointwise boundary values on the original tube submanifold. The $C^k$-norm of the extension is shown to be no bigger than the $C^k$-norm of the original CR function.