Heat a grill over high heat. Season the chicken with vegetable oil, salt and pepper. Grill until nicely charred on one side, about 3 minutes, then turn and repeat on the second side. Lower heat to medium and continue to cook, turning from time to time until the chicken is cooked through, about 15 minutes altogether. When cool enough to handle, chop or shred the chicken and place in a large bowl.
Meanwhile, bring a large pot of salted water to a boil. Cook the pasta according to package directions to al dente. Drain, rinse under cold water to stop the cooking. Add to a bowl along with the zucchini, yellow squash, and tomato vegetable medley.
In a separate bowl, combine the lemon juice, basil, capers, and garlic. Whisk in the olive oil then toss with all of the other ingredients. Season to taste with salt and pepper.