How to Make It
Preheat oven to 500°.
Split chicken in half lengthwise. Heat canola oil in a large stainless steel skillet over high heat. Place chicken, skin side down, in pan; place pan in oven. Cook chicken at 500° for 10 minutes; remove from oven. Carefully turn chicken over; pour 1 1/2 cups broth over chicken. Return pan to oven; cook an additional 25 minutes or until a thermometer inserted in the meaty part of thigh registers 165°. Remove chicken from pan; let stand 10 minutes. Remove skin from chicken; discard skin. Sprinkle chicken with 1/4 teaspoon salt and 1/4 teaspoon pepper; slice chicken. Cover and keep warm.
Combine 3 cups water and juice in a large bowl. Working with 1 artichoke at a time, cut off stem to within 1/4-inch from the base; peel stem. Remove bottom leaves and tough outer leaves, leaving tender heart and bottom; trim about 1 inch from top of artichoke. Cut each artichoke lengthwise into quarters. Place artichoke quarters in lemon water.
Heat olive oil in a large skillet over medium heat. Drain artichokes well; pat dry. Add artichokes to pan. Cover and cook 10 minutes or until tender; uncover. Increase heat to high; cook 2 minutes or until artichokes are golden, stirring frequently. Place artichokes in a medium bowl; sprinkle with remaining 1/4 teaspoon salt and remaining 1/4 teaspoon pepper.
Place a zip-top plastic bag inside a 2-cup glass measure. Pour chicken drippings into bag; let stand 10 minutes (fat will rise to the top). Seal bag; carefully snip off 1 bottom corner of bag. Place pan over medium-high heat. Drain drippings into pan, stopping before fat layer reaches opening; discard fat. Stir in wine. Bring to a boil; cook until reduced to 1 cup (about 8 minutes).
Combine remaining 2 tablespoons broth and flour, stirring until smooth. Add flour mixture to drippings; bring to a boil. Reduce heat to medium-low. Add artichokes, capers, and olives; cook 2 minutes or until thoroughly heated, stirring frequently. Serve with chicken and rice.