Place chicken between plastic wrap; pound with meat mallet or rolling pin to 1/4-inch thickness. Sprinkle chicken with salt and black pepper.
Combine butter, parsley, oregano, rosemary and basil in small bowl. Place 1-1/2 teaspoons herb butter on centers of breast halves, reserving remaining herb butter.
Place one cheese strip in center of each breast half. Roll up chicken with cheese inside; tuck in ends. Roll in flour, then dip in egg. Coat with breadcrumbs. Place in ungreased 13x9-inch baking dish; bake at 375 degrees 15 minutes.
Stir wine into remaining herb butter in small saucepan; heat over low heat until butter melts. Pour over chicken; bake 20 minutes more.
Heat oil in large skillet over medium heat until hot. Add red and green bell peppers; cook and stir until crisp-tender. Add rice; toss lightly. Heat thoroughly. Serve chicken over rice.
Pour pan drippings into small saucepan. Dissolve cornstarch in water. Add to drippings; heat until mixture boils and thickens, stirring constantly. Serve with chicken and rice. Garnish with oregano and rosemary.