  A result of Seymour implies that any 3-connected matroid with a modular
3-point line is binary. We prove a similar characterization for 3-connected
matroids with modular 4-point lines. We show that such a matroid is either
representable over GF(3) or GF(4) or has an $F_7$-minor and either an
$(F_7^-)$- or $(F_7^-)^*$-minor.
