Pat the chicken pieces dry and season lightly with salt and pepper.
Heat 1 tablespoon of olive oil in a large skillet over medium-high heat. Add the chicken and cook undisturbed for 3–4 minutes, then stir and cook until browned and mostly cooked through, about 2–3 more minutes. Transfer the chicken to a plate.
Add the remaining 1 tablespoon olive oil to the skillet. Sauté the sliced zucchini, red bell pepper, and sliced onion for 3–4 minutes until slightly softened but still firm.
Add the minced garlic and grated ginger to the vegetables and cook for 1 minute until fragrant.
Pour in the coconut milk, then whisk in the Thai red curry paste and fish sauce until smooth. Bring the mixture to a gentle boil.
Reduce the heat to a simmer, return the chicken to the skillet, and cook for a few minutes until the chicken is cooked through and the sauce is slightly thickened.
Stir in the lime juice, taste, and adjust seasoning with more lime juice, fish sauce, or salt if desired. Serve immediately.
