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An algorithm for inverting extended gravitational lens images using the maximum entropy method is presented. In one dimensional tests, this method accurately inverts ring-type images and is effective at solving for the unknown lens parameters. No a priori assumptions are made about the structure of the source, and an objective test of goodness of fit is used to check the accuracy of the inversion. For certain sources which are large compared to the lens critical radius, systematic ``glitches" occur in the reconstruction at the boundaries separating different image multiplicities. These errors are found to be intrinsic to MEM when applied to lensing, and may occur in all lens reconstruction methods, but they can be removed with filtering. Two dimensional tests on real data are discussed, and show this method to be quite promising.
