The Lomb-Scargle periodogram has long been a workhorse in astronomy for detecting periodicity from irregularly sampled observations of variable sources. The classic periodogram cannot, however, make use of the multi-band photometry of many current and future surveys. While past studies have used K-corrections and/or ad hoc methods to address this, a more principled approach will become necessary for future surveys. Our solution is the multiband periodogram, a generalization of the classic Lomb-Scargle method which flexibly accounts for multi-band observations within a single model, without any physical assumptions about corrections between bands. Experiments on simulated data indicate that this new method vastly improves on previous approaches, pushing the effective limit of LSST RR Lyrae studies 1-2 magnitudes deeper.