Preheat the grill to medium-high (about 400°F).
Grill the chicken breasts directly over heat for 6–8 minutes per side, until an instant-read thermometer registers 160–165°F in the thickest part.
Remove the chicken from the grill and let rest 5 minutes, then slice thinly.
Grill the corn until slightly charred on all sides, then remove kernels from the cob.
Arrange the salad greens on a large platter or place in a large bowl.
Top the greens with sliced grilled chicken, corn kernels, drained black beans, halved cherry tomatoes, thinly sliced red onion, crushed tortilla chips, and torn cilantro.
Place the salsa in a small bowl alongside the salad; either serve the avocado halved next to the salad or dice it and toss it into the salad.
Slice the lime and squeeze fresh lime juice over the salad just before serving.