Preheat the oven to 425°F (220°C). Line a large baking sheet with foil and place the sheet in the oven to heat while you prepare the ingredients. Use oven mitts when handling the hot sheet.
Trim any fat from the 3 boneless, skinless chicken breasts and cut them into pieces at least 1 inch square.
Trim the ends from the 2 cups sugar snap peas.
Cut the 2 red bell peppers in half, remove and discard the core and seeds, then cut the peppers into strips about the same thickness as the sugar snap peas.
Put the prepared vegetables (bell pepper strips and sugar snap peas) into a bowl and toss them with the 1 1/2 tablespoons peanut oil until evenly coated.
Carefully remove the hot baking sheet from the oven. Arrange the chicken pieces in a single layer on the sheet, spacing them so pieces are not touching.
Return the baking sheet to the oven and cook the chicken 8 minutes.
Remove the baking sheet and arrange the oiled vegetables around the chicken in a single layer, pressing pieces so they touch the pan where possible.
Return the sheet to the oven and cook about 12 minutes more, or until the chicken is cooked through and lightly browned (juices run clear and no pink remains).
Remove the sheet from the oven, sprinkle the cooked chicken and vegetables with 1–2 tablespoons sesame seeds, preferably black, and serve hot.