  We demonstrate a novel means of creating Majorana zero modes using magnetic
flux applied to a full superconducting shell surrounding a semiconducting
nanowire core, unifying approaches based on proximitized nanowires and vortices
in topological superconductors. In the destructive Little-Parks regime,
reentrant regions of superconductivity are associated with integer number of
phase windings in the shell. Tunneling into the core reveals a hard induced gap
near zero applied flux, corresponding to zero phase winding, and a gapped
region with a discrete zero-energy state for flux around {\Phi}_0 = h/2e,
corresponding to 2{\pi} phase winding. Coulomb peak spacing in full-shell
islands around one applied flux shows exponentially decreasing deviation from
1e periodicity with device length, consistent with the picture of Majorana
modes located at the ends of the wire.
