© 2016. The American Astronomical Society. All rights reserved. Type Ia supernovae (SNe Ia) that are multiply imaged by gravitational lensing can extend the SN Ia Hubble diagram to very high redshifts (z ≳ 2), probe potential SN Ia evolution, and deliver high-precision constraints on H0, w, and Ωmvia time delays. However, only one, iPTF16geu, has been found to date, and many more are needed to achieve these goals. To increase the multiply imaged SN Ia discovery rate, we present a simple algorithm for identifying gravitationally lensed SN Ia candidates in cadenced, wide-field optical imaging surveys. The technique is to look for supernovae that appear to be hosted by elliptical galaxies, but that have absolute magnitudes implied by the apparent hosts' photometric redshifts that are far brighter than the absolute magnitudes of normal SNe Ia (the brightest type of supernovae found in elliptical galaxies). Importantly, this purely photometric method does not require the ability to resolve the lensed images for discovery. Active galactic nuclei, the primary sources of contamination that affect the method, can be controlled using catalog cross-matches and color cuts. Highly magnified core-collapse SNe will also be discovered as a byproduct of the method. Using a Monte Carlo simulation, we forecast that the Large Synoptic Survey Telescope can discover up to 500 multiply imaged SNe Ia using this technique in a 10 year z-band search, more than an order of magnitude improvement over previous estimates. We also predict that the Zwicky Transient Facility should find up to 10 multiply imaged SNe Ia using this technique in a 3 year R-band search - despite the fact that this survey will not resolve a single system.