Heat the vegetable oil in a skillet over high heat for a minute or so. Add the chicken breast and cook 4 to 5 minutes on each side, until golden brown. Transfer the chicken to a roasting pan, reserving the drippings in the skillet.
Pour the broth over the chicken in the roasting pan. Cover the roasting pan and bake for 20 minutes, until chicken reaches an internal temperature of 170°.
While the chicken is cooking, add the orange, grapefruit, marmalade, lime juice, and red pepper to the skillet with the drippings and whisk. Simmer for 5 minutes.
For each serving, place chicken on a plate and ladle ¼ cup of sauce over top.