Make the sauce: In a bowl, whisk pineapple juice, soy sauce, ketchup, vinegar, brown sugar (or honey), tomato paste, sesame oil, and chili flakes if using.
Set aside. Stir together cornstarch and water in a separate small bowl.
Prep the chicken: Pat the chicken dry with paper towels and season lightly with salt and pepper. This helps it brown well and keeps the sauce from becoming too salty.
Sear the chicken: Heat oil in a large skillet over medium-high.
Add the chicken in a single layer. Cook 5–7 minutes, turning once, until lightly browned and just cooked through. Transfer to a plate.
Sauté aromatics: In the same skillet, add a touch more oil if needed.
Add garlic, ginger, and the white parts of the green onions. Cook 30–45 seconds until fragrant.
Cook the peppers and pineapple: Add the red bell pepper and sauté 2 minutes to soften slightly. Stir in pineapple chunks and cook 1–2 minutes to warm and caramelize a bit.
Glaze it up: Return the chicken to the skillet.
Pour in the sauce and bring to a gentle simmer. Stir the cornstarch slurry, then drizzle it in while stirring. Simmer 1–2 minutes until the sauce turns glossy and thick.
Finish with lime: Turn off the heat.
Stir in lime juice and the green parts of the green onions. Taste and adjust sweetness, salt, or acidity as needed.
Serve: Spoon over hot rice. Top with sesame seeds and a squeeze of lime.
Enjoy immediately.