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We observed 12 Plutinos over two separated years with the 4.3 m Lowell’s Discovery Channel Telescope. Here, we present the first light-curve data for those objects. Three of them (2014 JL80, 2014 JO80, and 2014 JQ80) display a large light-curve amplitude explainable by a single elongated object, but they are most likely caused by a contact binary system due to their light-curve morphology. These potential contact binaries have rotational periods from 6.3 to 34.9 hr and peak-to-peak light-curve variability between 0.6 and 0.8mag. We present partial light curves, allowing us to constrain the light-curve amplitude and the rotational period of another nine Plutinos. By merging our data with the literature, we estimate that up to ∼40% of the Plutinos could be contact binaries. Interestingly, we found that all of the suspected contact binaries in the 3:2 resonance are small with absolute magnitude H>6mag. Based on our sample and the literature, up to ∼50% of the small Plutinos are potential contact binaries.