  We define Chern-Schwartz-MacPherson (CSM) cycles of an arbitrary matroid.
These are balanced weighted fans supported on the skeleta of the corresponding
Bergman fan. In the case that the matroid arises from a complex hyperplane
arrangement A, we show that these cycles represent the CSM class of the
complement of A. We also prove that for any matroid, the degrees of its CSM
cycles are given by the coefficients of (a shift of) the reduced characteristic
polynomial, and that CSM cycles are valuations under matroid polytope
subdivisions.
