Cook rice according to package directions, omitting salt and fat. Keep warm.
Combine sugar and next 4 ingredients (through ginger) in a small bowl. Heat a large nonstick skillet over medium-high heat. Coat pan with cooking spray. Add oil to pan. Add carrots and pepper to pan; sauté 2 minutes. Add chicken and peas to pan; sauté 1 minute. Transfer chicken mixture to a large bowl; stir in salt.
Return pan to heat. Add soy sauce mixture to pan; bring to a boil. Cook until reduced to 1/4 cup (about 1 1/2 minutes), stirring constantly. Arrange about 1/2 cup rice on each of 4 plates; top each serving with about 1 1/4 cups chicken mixture. Drizzle 1 tablespoon sauce over each serving; sprinkle each serving with about 4 teaspoons peanuts.