  In this note we introduce certain invariants of real Lefschetz fibrations. We
call these invariants {\em real Lefschetz chains}. We prove that if the fiber
genus is greater than 1, then the real Lefschetz chains are complete invariants
of real Lefschetz fibrations with only real critical values. If however the
fiber genus is 1, real Lefschetz chains are not sufficient to distinguish real
Lefschetz fibrations. We show that by adding a certain binary decoration to
real Lefschetz chains, we get a complete invariant.
