  We characterise finite groups such that for an odd prime $p$ all the
irreducible characters in its principal $p$-block have odd degree. We show that
this situation does not occur in non-abelian simple groups of order divisible
by $p$ unless $p=7$ and the group is $M_{22}$. As a consequence we deduce that
if $p\neq 7$ or if $M_{22}$ is not a composition factor of a group $G$, then
the condition above is equivalent to $G/O_{p'}(G)$ having odd order.
