  A graph $G$ is \emph{chordless} if no cycle in $G$ has a chord. In the
present work we investigate the chromatic index and total chromatic number of
chordless graphs. We describe a known decomposition result for chordless graphs
and use it to establish that every chordless graph of maximum degree
$\Delta\geq 3$ has chromatic index $\Delta$ and total chromatic number $\Delta
+ 1$. The proofs are algorithmic in the sense that we actually output an
optimal colouring of a graph instance in polynomial time.
