Add the rice vinegar, blackberries, honey, ginger, lemongrass, sesame oil, salt, and pepper to a food processor or blender.
Blend until the mixture is smooth and well combined. Set the blackberry sauce aside.
Pat the salmon fillets dry with paper towels. Brush each fillet evenly with chili garlic sauce.
Preheat a grill to medium heat. Oil the grill grates well to help prevent the salmon from sticking.
Place the salmon on the grill and cook for about 5 minutes per side, depending on thickness and desired doneness.
Remove the salmon from the grill and let it rest for about 5 minutes.
Check that the salmon flakes easily with a fork and is cooked to your preferred level of doneness.
Serve the Grilled Salmon with Blackberry Sauce alongside your favorite green vegetable.