Combine lemon slices, sugar, and garlic in a medium bowl.
Sprinkle chicken with 3/8 teaspoon salt and pepper.
Heat a large skillet over medium-high heat.
Add 2 teaspoons oil.
Add chicken to pan; cook 4 minutes on each side or until done.
Place chicken on a plate.
Add remaining 1 teaspoon oil to pan.
Add lemon mixture to pan; cook 1 minute or until lemon slices are lightly browned, turning occasionally.
Return lemon mixture to bowl.
Wipe pan with paper towels.
Heat pan over medium heat.
Add 1 1/2 teaspoons butter to pan.
Add shallot, 1/2 teaspoon grated garlic, oregano sprig, and thyme sprig; cook 1 minute.
Add wine to pan, scraping pan to loosen browned bits.
Bring to a boil; cook 3 minutes or until liquid almost evaporates.
Add remaining 1/8 teaspoon salt, stock, and flour to pan, stirring with a whisk.
Bring to a boil; reduce heat, and simmer 3 minutes or until liquid is reduced to about 2/3 cup.
Remove pan from heat; discard oregano and thyme sprigs.
Stir in remaining 1 1/2 tablespoons butter and capers, stirring until butter melts.
Return chicken and any juices to pan; turn to coat with sauce.
Top chicken with lemon mixture. Sprinkle with parsley.
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