In a small bowl, combine blackberries, cucumber, green onion and 1 tablespoon chili sauce; toss to coat. Sprinkle salmon with salt and pepper.
Place fillets on greased grill rack, skin side down. Grill, covered, over medium-high heat or broil 4 in. from heat 10-12 minutes or until fish flakes easily with a fork, brushing with remaining chili sauce during the last 2-3 minutes of cooking. Serve with blackberry mixture.