  Let $\mathfrak{g}$ be a finite-dimensional simple Lie algebra over
$\mathbb{C}$. In the 1950s Chevalley showed that $\mathfrak{g}$ admits
particular bases, now called ``Chevalley bases'', for which the corresponding
structure constants are integers. Such bases are not unique but, using
Lusztig's theory of canonical bases, one can single out a ``canonical''
Chevalley basis which is unique up to a global sign. In this paper, we give
explicit formulae for the structure constants with respect to such a basis.
