Preheat the oven to 375°F (190°C).
Arrange the chicken breasts in a single layer on a rimmed baking sheet or in a large oven-safe skillet.
Drizzle the chicken evenly with 2 teaspoons olive oil and rub to coat.
Bake the chicken until the internal temperature reaches 165°F (74°C) and the juices run clear when pierced, about 20–30 minutes depending on thickness.
Remove the chicken from the oven and spread a generous layer of Southern pimento cheese over each piece.
Return the chicken to the oven and bake until the cheese is melted and warmed through, about 8–10 minutes.
Let the chicken rest a few minutes before serving.