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1
Core tomatoes and cut a shallow X in bottom of each, then blanch in a medium pot of boiling water 10 seconds. Transfer with a slotted spoon to an ice bath to stop cooking. Peel, seed, and finely chop.
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2
Pat chicken dry and sprinkle with 1/2 teaspoon each of salt and pepper, then dredge in flour, shaking off excess.
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3
Heat oil in a 12-inch heavy skillet over medium-high heat until it shimmers, then cook chicken, turning once, until golden and just cooked through, 6 to 8 minutes total. Transfer to a platter and keep warm, covered.
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4
Add garlic and anchovy paste to skillet and cook over medium heat, stirring, until fragrant, about 30 seconds. Add wine and bring to a boil, scraping up brown bits. Stir in tomatoes, stock, and olives and simmer, uncovered, stirring occasionally, until mixture has thickened into a sauce, 8 to 10 minutes. Whisk in butter and any juices from platter.
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5
Add chicken and simmer until just heated through, about 1 minute. Serve sprinkled with basil.
