Let $X$ be a normal connected noetherian scheme of finite dimension and let $Z \subset X$ be a closed subset of codimension at least 2. Is the canonical map $$Pic(X) \to Pic(X \setminus Z)$$ an isomorphism?
Background: The statement is true for regular schemes $X$, as there we can express $Pic(X)$ in terms of Weil Divisors up to rational equivalence. Motivated by this and the fact that normal schemes are regular in codimension 1, one might hope that one can extend this statement to normal schemes.