Pound chicken breasts to even 1/2-inch thickness. Combine butter and 1 tablespoon oil in shallow bowl. Put crushed croutons in pie plate. Dip chicken breasts in butter mixture, then croutons, shaking off excess.
Heat remaining 1 tablespoon oil in large skillet over medium-high heat. Add coated chicken. Cook until brown, about 3 minutes per side. Reduce heat to low. Cook 1 to 2 additional minutes per side until chicken is tender and no longer pink (170°F).
Combine goat cheese, half-and-half and chives with electric mixer at medium speed. Place each chicken piece on serving plate; top with a dollop of flavored goat cheese.
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