  We extend the classical Schubert calculus of enumerative geometry for the
Grassmann variety of lines in projective space from the complex realm to the
real. Specifically, given any collection of Schubert conditions on lines in
projective space which generically determine a finite number of lines, we show
there exist real generic conditions determining the expected number of real
lines. Our main tool is an explicit description of rational equivalences which
also constitutes a novel determination of the Chow rings of these Grassmann
varieties.
