Combine olive oil, honey, lemon juice, minced garlic, smoked paprika, salt, pepper, and fresh thyme in a small bowl. Whisk everything together until the honey dissolves completely. This marinade-style glaze is what makes the magic happen on the grill.
Pat your 4 chicken breasts dry with paper towels — this step is crucial for getting that golden sear. Brush both sides generously with half of your glaze mixture and set aside. Save the remaining glaze for brushing on halfway through cooking.
Preheat your grill to medium-high heat (about 375°F). Oil the grates well so nothing sticks. I like to use a balled-up paper towel dipped in oil to coat the grates right before the chicken goes on.
Place chicken breasts on the grill and don't move them for 6-7 minutes. You'll hear it sizzle when it first hits the grates — that's exactly what you want. Resist the urge to flip early; that's how you get those beautiful grill marks.
Flip the chicken and brush with your remaining glaze. Grill for another 6-7 minutes until the internal temperature reaches 165°F at the thickest part. Mine always cooks a bit unevenly depending on breast thickness, so I check multiple spots.
During the last 2 minutes of cooking, place your peach halves cut-side down on the grill. They need just 1-2 minutes per side to get caramelized and warm through. Watch them closely — they go from perfect to overly soft pretty fast.
Remove everything from the grill and let the chicken rest for 3-4 minutes before serving. Top each breast with grilled peach halves, fresh arugula, and toasted pistachios. The warm chicken against the cool peppery greens creates the perfect contrast.