Sprinkle chicken with paprika, 1/4 teaspoon pepper and 1/8 teaspoon salt. Heat oil in a large skillet over medium-high heat until shimmering. Add the chicken and cook, flipping halfway, until golden brown and an instant-read thermometer inserted in the thickest part registers 165°F, 6 to 8 minutes. Transfer to a plate.
Meanwhile, soak currants in water for 5 minutes; drain. Combine the currants, arugula, roasted peppers, pine nuts, sugar, garlic, vinegar and the remaining 1/4 teaspoon pepper and pinch of salt in a small bowl. Serve with the chicken.