  Let G be a finite simple graph. From the pioneering work of R. P. Stanley it
is known that the cycle matroid of G is supersolvable iff G is chordal (rigid):
this is another way to read Dirac's theorem on chordal graphs. Chordal binary
matroids are not in general supersolvable. Nevertheless we prove that, for
every supersolvable binary matroid M, a maximal chain of modular flats of M
canonically determines a chordal graph.
