In a high-speed blender, combine fresh blackberries, balsamic vinegar, olive oil, honey, Dijon mustard, salt, and thyme. Blend until smooth, about 30 seconds.

Strain the mixture through a fine-mesh sieve into a bowl, discarding the seeds.

Reserve about two-thirds of the blackberry mixture for later use as a dressing.

Marinate the boneless skinless chicken breasts in the remaining blackberry mixture, cover, and refrigerate for at least 30 minutes or up to overnight.

Preheat the grill to medium heat, around 350°F to 400°F.

Grill the marinated chicken for 20 to 25 minutes, flipping occasionally until the internal temperature reaches 165°F.

While the chicken rests, prepare the salad base with fresh arugula and torn basil leaves.

Slice the grilled chicken and layer it on top of the greens with creamy avocado slices and fresh blackberries.

Sprinkle with toasted pumpkin seeds and drizzle with the reserved blackberry vinaigrette.

Serve immediately.