In a medium saucepan, combine 3/4 cup sweet Thai chile sauce, 1/4 cup soy sauce, 1 tablespoon creamy peanut butter, 2 tablespoons pomegranate juice, 1 tablespoon rice vinegar, juice of 1 lime, 1 teaspoon fish sauce (optional), 1–2 cloves minced garlic, and 2 teaspoons grated ginger.
Bring the sauce to a boil over medium-high heat, then reduce heat and simmer 5–10 minutes until slightly thickened; remove from heat and set aside.
Toss the shredded cooked chicken and thinly sliced red bell pepper in a bowl with the Thai chile sauce until evenly coated.
Remove the thick stems from the Swiss chard leaves so they lie flat.
Spoon about 1 tablespoon of the peanut-ginger sauce down the center of each chard leaf.
Place a spoonful of the chicken and pepper mixture in the center of each leaf, add a handful of pomegranate arils, and sprinkle with fresh cilantro and toasted sesame seeds.
Roll the chard leaves to enclose the filling and serve the wraps with the remaining peanut-ginger sauce for dipping.
To make the peanut-ginger sauce: whisk together 1/3 cup peanut butter, 2 tablespoons soy sauce or tamari, 2 teaspoons grated ginger, and 1 tablespoon rice vinegar; thin with 2–4 tablespoons water to desired consistency.