Heat 1 tablespoon of the oil in a large skillet over medium heat. Season the chicken with the paprika, cumin, ½ teaspoon salt, and ¼ teaspoon pepper.
Cook the chicken until golden brown and cooked through, 6 to 7 minutes per side. Transfer to a cutting board.
Meanwhile, place the couscous in a large bowl. Add 1 cup hot tap water, cover, and let sit for 5 minutes. Fluff with a fork.
Add the tomatoes, snap peas, basil, lemon zest and juice, remaining oil, ½ teaspoon salt, and ¼ teaspoon pepper to couscous. Toss to combine.
Slice the chicken and serve with the couscous.