In a cup, dissolve cornstarch in broth and set aside.
Melt 2 Tablespoons of butter in a 1-quart saucepan over medium-low heat. Add garlic and onion; cook, stirring constantly, until they are limp and slightly golden. Add additional ¼ cup butter; allow butter to melt. Whisk broth mixture, lemon juice, and wine into melted butter.
Continue to cook until sauce thickens. Add capers. Serve sauce over grilled or broiled chicken breasts.
Note: This buttery lemon sauce is also great over grilled or broiled fish.