Heat 1 lbsp. oil in medium skillet over medium heat; add chicken. Cook, stirring until chicken is cooked through, about 5 minutes. Remove from skillet and drain on paper towels.
Heat remaininig oil in same skillet. Begin heating water for pasta. Add carrot to skillet; cook stirring, for 4 minutes. Add broccoli and garlic to skillet; cook, stirring, for 2 minutes longer.
Cook pasta according to package directions. While pasta is cooking, add chicken broth, and basil to skillet. Stir to combine. Return chicken to skillet. Reduce heat and simmer for 4 minutes.
Drain pasta. Place in a large serving bowl. Top with chicken and vegetable mixture. Serve immediately
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