Nondissipative transport of strangeness is studied in a chiral hadronic plasma with three flavors. In the phase in which chiral symmetry is preserved, strangeness transport is found to be driven by both an external magnetic field and fluid vorticity. As for the constitutive relations of the baryon and electromagnetic currents, they exhibit vortical terms proportional to the strangeness chemical potential. In the superfluid phase, transverse nondissipative diffusion of the baryon, electromagnetic, and strangeness charges is found, which survives in the limit of vanishing chiral imbalance and mixes in a fashion similar to standard dissipative diffusion in quark-gluon plasma.