Pound chicken to even 0.5-inch thinkness. Dredge chicken in flour.
Melt 1 Tbs butter over medium-high heat and add 1 Tbs oil. Add chicken to pan; saute 4 minutes on each side or until done. Remove chicken from pan; keep warm.
Heat 1 Tbs oil in pan. Add shallots to pan, saute 3 minutes. Add garlic, saute 1 minute. Add wine, bring to a boil, scraping pan to loosen browned bits. Cook until liquid almost evaporates, stirring occasionally. Add 0.5 cup broth, bring to a boil, and cook until reduced by half (about 5 minutes) Stir together 0.25 cups broth with 1 tsp four until smooth, then add to pan. Cook 1 minute or until slightly thickened. Remove from heat and stir in remaining 1.5 Tbs butter, juice, and capers. Sprinkle with parsley and serve.