Heat 1 T. oil in a medium skillet over medium heat; add chicken. Cook, stirring, until chicken is cook thoroughly - about 5 minutes. Remove from skillet and drain on paper towels.
Heat remaining oil in same skillet. Begin heating water for pasta. Add carot 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, basil and Parmesan 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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