In a large bowl or zip-top bag, combine the chicken, Italian vinaigrette, and lime juice. Marinate for at least 5 minutes while the grill heats, or up to 1 hour in the refrigerator.
Preheat the grill to medium-high heat.
Add the corn, asparagus, and red onion to a large bowl. Toss with olive oil and a generous pinch of sea salt. Transfer the vegetables to a grill basket.
Grill the chicken for 5–7 minutes per side, or until cooked through and the internal temperature reaches 165°F. Transfer to a cutting board and let rest before slicing.
Place the grill basket on the grill alongside the chicken. Cook, stirring occasionally, until the vegetables are tender and lightly charred, about 10–12 minutes.
Meanwhile, cook the pasta according to package directions. Drain and rinse under cold water to cool completely.
In a small bowl, whisk together the olive oil and pesto until smooth.
Add the cooked pasta, grilled vegetables, and sliced chicken to a large serving bowl. Pour the pesto dressing over the top and toss until evenly coated.
Season with freshly ground black pepper and additional sea salt to taste.
Serve immediately or refrigerate in an airtight container for up to 4 days until ready to serve. Enjoy!