Mix raw cubed chicken with 1 Tbsp garlic, 1 Tbsp ginger, and 2 Tbsp soy sauce. Leave to marinate while you prep the veggies.
Make sauce mix: You should have about 2/3 cup pineapple juice (add chicken broth if you need to make 2/3 cup). In a bowl, combine pineapple juice, chicken broth, brown & white sugars, vinegar, cornstarch, and remaining soy sauce. Salt to taste and set aside.
Place large nonstick skillet or wok over medium-high heat. When pan is hot add 2 Tbsp cooking oil and chicken (discard marinade). Brown chicken cubes, then remove from pan and keep warm. Wipe out skillet with paper towel then add remaining 1 Tbsp oil. Add carrots, onion, bell-pepper, and the remaining garlic and ginger; stir-fry for 3 minutes. Add snow peas and stir-fry for about 2 more minutes. The veggies should be crisp-tender.
Add pineapple chunks and sauce mix to pan. Add reserved chicken cubes. Bring to a simmer and cook until sauce thickens.