Increase bandwidth (but SNR decreases). This reduces the size of the artefact. Increasing the magnitude of the read-out gradient is equivalent.
Swap the frequency-encode and phase-encoding directions. This will not eliminate the chemical shift artefact but will rotate it to another anatomical area. This may also cause phase wraparound or flow-related artefacts to be shifted over the region of interest too.
(Lower the external magnetic field strength....this is not a realistic option!)