We present a new algorithm for constructing a Chevalley basis for any
Chevalley Lie algebra over a finite field. This is a necessary component for
some constructive recognition algorithms of exceptional quasisimple groups of
Lie type. When applied to a simple Chevalley Lie algebra in characteristic at
least 5, our algorithm has complexity involving the 7th power of the Lie rank,
which is likely to be close to best possible
