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In a large saucepan, melt the butter over low heat. Add the minced garlic and cook for about a minute.
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Add the tomatoes and 3/4 cup of the chicken broth. Increase the heat to medium and bring the mixture to a boil. Reduce the heat and simmer uncovered, for about 10 minutes.
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Add the cream and bring to a boil again, stirring frequently. Simmer over medium heat until the sauce is thick.
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Sprinkle salt and pepper over both sides of the chicken.
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Heat the olive oil in a skillet, then add the chicken and saute until it's is no longer pink inside.
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(About 4 minutes each side should do it.) Remove the chicken from the skillet and drain the fat from the skillet.
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In the same skillet, stir 1/4 cup chicken broth with the pan juices, and bring to a boil; reduce the heat slightly and add to the cream sauce; stir in basil.
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Serve chicken atop the pasta, coat with the cream sauce.