The spontaneous breaking of $U(1)_{B-L}$ around the scale of grand unification can simultaneously account for hybrid inflation, leptogenesis, and neutralino dark matter, thus resolving three major puzzles of particle physics and cosmology in a single predictive framework. The B-L phase transition also results in a network of cosmic strings. If strong and electroweak interactions are unified in an SO(10) gauge group, containing $U(1)_{B-L}$ as a subgroup, these strings are metastable. In this case, they produce a stochastic background of gravitational waves that evades current pulsar timing bounds, but features a flat spectrum with amplitude $h^2\Omega_\text{GW} \sim 10^{-8}$ at interferometer frequencies. Ongoing and future LIGO observations will hence probe the scale of B-L breaking.