Erdős Problem #832 — Minimum edges in a high-chromatic uniform hypergraph

For fixed $r\geq3$ and all sufficiently large $k$, must every $r$-uniform hypergraph of chromatic number $k$ have at least $\binom{(r-1)(k-1)+1}{r}$ edges, with equality only for the complete $r$-uniform hypergraph on $(r-1)(k-1)+1$ vertices?