Place each chicken breast half between 2 sheets of heavy-duty plastic wrap; pound each piece to 1/4-inch thickness using a meat mallet or small heavy skillet.
Melt butter and oil in a large nonstick skillet over low heat.
Combine flour, cumin, and salt in a shallow dish. Dip chicken in orange juice concentrate; dredge in flour mixture. Reserve concentrate.
Increase heat to medium-high. Heat pan for 2 minutes or until butter starts to brown. Add chicken; cook 3 minutes on each side or until done. Remove from pan; keep warm.
Stir in reserved concentrate, 1/2 cup water, and chile. Bring to a boil; cook 2 minutes. (Thin sauce with 2 tablespoons water, if needed.)
Combine rice and chopped cilantro. Serve with chicken. Garnish with cilantro sprigs, if desired.