  We prove that for $n>k\geq 3$, if $G$ is an $n$-vertex graph with chromatic
number $k$ but any its proper subgraph has smaller chromatic number, then $G$
contains at most $n-k+3$ copies of cliques of size $k-1$. This answers a
problem of Abbott and Zhou and provides a tight bound on a conjecture of
Gallai.
