In small saucepan, combine chicken broth and drained cherry juice. Boil over high heat and reduce to ½ cup.
In small bowl, combine port and dried cherries. Reserve. In small bowl, blend together flour and 1 tablespoon butter to make smooth paste. Reserve.
While broth mixture is reducing, sprinkle salt and pepper on chicken. In large sauté pan, melt remaining butter and olive oil over medium heat. Brown cutlets until golden, about 3 minutes per side. Remove to plate and cover with foil.
In the same pan, add shallots and sauté until soft and translucent, about 1 minute. Add port and dried cherries. Stir to scrape up browned bits on bottom of pan. Bring to a boil and reduce slightly by boiling for about 1 minute. Add reduced broth/ cherry juice and lemon juice and boil for another minute.
Stir flour/ butter mixture into the sauce. Cook over medium heat for about 2 minutes, or until sauce is slightly thickened. Add cherries and thyme to pan. Stir to combine. Return chicken to pan along with any accumulated juices. Warm for one minute.
Serve chicken cutlets over wild or brown rice. Spoon sauce and cherries over cutlets.