Let $r\ge 3$ and $k$ be sufficiently large in terms of $r$. Is it true that every $r$-uniform hypergraph with chromatic number $k$ has at least$$\left(\genfrac{}{}{0ex}{}{(r-1)(k-1)+1}{r}\right)$$edges, with equality only for the complete graph on $(r-1)(k-1)+1$ vertices?