To prepare chicken, combine first 6 ingredients in a large bowl. Add chicken to basil mixture, turning to coat.
Heat a large nonstick skillet over medium-high heat. Coat pan with cooking spray. Add chicken to pan; cook 8 minutes on each side or until done.
While chicken cooks, prepare aioli. Combine 1/4 cup basil and remaining ingredients in a small bowl, stirring with a whisk. Serve with chicken.
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