Heat 1 tablespoon of the oil in a large skillet over medium heat. Season the chicken with blackening seasoning, ½ teaspoon salt, and ¼ teaspoon black pepper.
Cook the chicken until golden brown and cooked through, 6 to 7 minutes per side. Transfer to plates.
Meanwhile, in a second skillet, heat the remaining 3 tablespoons of oil over medium-high heat.
Add the garlic and bell pepper to the second skillet and cook, tossing frequently, until beginning to soften, 2 to 3 minutes.
Add the collard greens, ¾ teaspoon salt, and ¼ teaspoon pepper and cook, tossing, until just tender, 5 to 7 minutes.
Stir in the black-eyed peas and cook until heated through, for 1 to 2 minutes more. Serve with chicken.