Combine first 6 ingredients in a medium bowl. Add chicken to broth mixture, stirring to coat. Let stand 3 minutes.
Heat oil in a large nonstick skillet over medium-high heat. Drain chicken, reserving marinade. Add chicken to the pan; cook 4 minutes or until done, stirring frequently. Stir in the reserved marinade. Reduce heat; cook 1 minute or until slightly thickened. Remove pan from heat.
Combine greens and basil in a large bowl. Add chicken mixture, tossing to coat. Place 1 1/4 cups salad mixture on each of 4 plates. Top each serving with 2 tablespoons onion and 1 1/2 teaspoons peanuts. Serve immediately. Serve with lime wedges, if desired.
The pan sauce in this dish doubles as a piquant vinaigrette for the salad. Serve with crunchy breadsticks, if you wish.