  Let $G$ be a simple graph with maximum degree $\Delta(G)$. A subgraph $H$ of
$G$ is overfull if $|E(H)|>\Delta(G)\lfloor |V(H)|/2 \rfloor$. Chetwynd and
Hilton in 1985 conjectured that a graph $G$ on $n$ vertices with
$\Delta(G)>n/3$ has chromatic index $\Delta(G)$ if and only if $G$ contains no
overfull subgraph. Glock, K\"{u}hn and Osthus in 2016 showed that the
conjecture is true for dense quasirandom graphs with even order, and they
conjectured that the same should hold for such graphs with odd order. In this
paper, we show that the conjecture of Glock, K\"{u}hn and Osthus is
affirmative.
