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We report the discovery of what is potentially ``relic" radio emission associated with the radio galaxy 3C 388. Here, we define relic radio emission as that emission produced by a radio plasma in a previous epoch of AGN activity, whose relativistic electron population has aged via synchrotron radiation. Until now, the few proposed relic radio sources have been diffuse, large ($>$200 Mpc), moderately polarized ($>$20\%), steep spectrum ($\alpha >$ 1.0), quasilinear structures with only a tentative identification for the host galaxy. Previous images of 3C 388 generated using the NRAO Very Large Array (VLA) revealed an unusual morphology which includes extended low surface brightness, highly polarized (20 to 50\%), steep spectrum ($\alpha\sim$1.5) emission. We have reobserved this unique radio source generating new 6 and 20 cm images which are both higher in resolution and dynamic range than previous images. These new images reveal a variety of interesting substructures which provide further support to the idea that the steep spectrum lobes of 3C 388 are radio relics resulting from intermittent jet activity. Both lobes of 3C 388 exhibit steep spectrum, relic emission and more typical flatter-spectrum radio emission separated by a well defined transition layer delineated by a dramatic jump in the spectral index which, at some locations, remains unresolved at 1.5$^{\prime\prime}$. We interpret these data as evidence of two distinct epochs of jet activity in which the current jets have resumed penetration of the IGM and are inflating younger, more energetic lobes into the relic lobes of the previous epoch. We also note that the observed asymmetries of the two lobes in 3C 388 can be explained by Doppler favoritism of mildly relativistic ($\beta \sim0.5$) jets and projection effects.
