This study will enroll approximately 100 adult subjects with moderate to severe plaque psoriasis involving palms and/or soles in approximately 20 centers in US and Canada. To be eligible, subjects must have moderate to severe plaque psoriasis involving palms or soles, with lesions covering at least 10% of the surface of palms and soles at the baseline visit. Study treatments will be assigned randomly (like flipping a coin) at a 1:1 ratio, meaning that there will be a 1 in 2 chance of either receiving Apremilast or placebo during the first 16 weeks. Subjects will not know which of the two treatments they receive. The study doctor, the study staff will not know which treatment they receive either. All subjects will receive Apremilast from Week 16 to Week 32.