Heat oil in a large skillet over medium high heat. Brown chicken on both sides and remove from skillet. Reserve.
To skillet add cranberries, blueberries, lemon juice, water, sugar and cornstarch. Mix together and bring to a boil, then reduce heat to medium low, stirring constantly.
Return chicken to skillet and simmer, covered, for 20 minutes. Remove cover, stir again and continue simmering until thick, adding salt to taste.
