  We extend the definition of chordal from graphs to clutters. The resulting
family generalizes both chordal graphs and matroids, and obeys many of the same
algebraic and geometric properties. Specifically, the independence complex of a
chordal clutter is shellable, hence sequentially Cohen-Macaulay; and the
circuit ideal of a certain complement to such a clutter has a linear
resolution. Minimal non-chordal clutters are also closely related to
obstructions to shellability, and we give some general families of such
obstructions, together with a classification by computation of all obstructions
to shellability on 6 vertices.
