Heat 1 tbsp oil in a saucepan over medium heat.
Add garlic and ginger, cook until fragrant (about 1 minute).
Stir in red curry paste, cook for 1 minute more.
Pour in coconut milk, bring to a simmer.
Stir in soy sauce and lime juice (and sugar, if using).
Simmer for a few minutes, then set the sauce aside.
In a large skillet or wok, heat 1 tbsp oil over medium-high heat.
Add the chicken and cook until browned and cooked through. Remove chicken from the skillet and set aside.
Add the sliced bell pepper and onion to the same skillet.
Sauté until the vegetables are tender-crisp, about 5-7 minutes.
Pour the red curry sauce back into the skillet with the peppers and onions.
Add the cooked chicken back into the sauce.
Stir in the fresh Thai basil leaves until they wilt slightly.
Spoon the red chicken curry over cooked rice. Enjoy immediately!