  We propose a new setup for creating Majorana bound states in a
two-dimensional electron gas Josephson junction. Our proposal relies
exclusively on a supercurrent parallel to the junction as a mechanism of
breaking time-reversal symmetry. We show that combined with spin-orbit
coupling, supercurrents induce a Zeeman-like spin splitting. Further, we
identify a new conserved quantity---charge-momentum parity---that prevents the
opening of the topological gap by the supercurrent in a straight Josephson
junction. We propose breaking this conservation law by adding a third
superconductor, introducing a periodic potential, or making the junction
zigzag-shaped. By comparing the topological phase diagrams and practical
limitations of these systems we identify the zigzag-shaped junction as the most
promising option.
