We use photometry from the DECam Legacy Survey to detect candidate tidal tails extending ∼5° on either side of the Palomar 13 globular cluster. The tails are aligned with the proper motion of Palomar 13 and are consistent with its old, metal-poor stellar population. We identify three RR Lyrae stars (RRLs) that are plausibly associated with the tails, in addition to four previously known in the cluster. From these RRLs, we find that the mean distance to the cluster and tails is 23.6 ± 0.2 kpc and estimate the total (initial) luminosity of the cluster to be ${L}_{V}={5.1}_{-3.4}^{+9.7}\times {10}^{3}\,{L}_{\odot }$, consistent with previous claims that its initial luminosity was higher than its current luminosity. Combined with previously determined proper motion and radial velocity measurements of the cluster, we find that Palomar 13 is on a highly eccentric orbit (e ∼ 0.8) with a pericenter of ∼9 kpc and an apocenter of ∼69 kpc, and a recent pericentric passage of the cluster ∼75 Myr ago. We note a prominent linear structure in the interstellar dust map that runs parallel to the candidate tidal features, but conclude that reddening due to dust is unlikely to account for the structure that we observe. If confirmed, the Palomar 13 stellar stream would be one of very few streams with a known progenitor system, making it uniquely powerful for studying the disruption of globular clusters, the formation of the stellar halo, and the distribution of matter within our Galaxy.