Gather all your ingredients. Dice your onion, chicken, zucchini, and shred the carrots. Mince the garlic and ginger, and set everything aside for easy access.
In a large pot or Dutch oven, heat coconut oil over medium heat. Add the diced onion and sauté until translucent, about 3-4 minutes. Stir in garlic and ginger, cooking for another minute until fragrant.
Add the diced chicken breast to the pot. Season with kosher salt and black pepper. Cook until the chicken is no longer pink, about 5-7 minutes.
Once the chicken is cooked through, add shredded carrots and diced zucchini. Stir well to combine, allowing the vegetables to soften for about 3-4 minutes.
Pour in the coconut milk and add the Thai green curry paste. Stir until the paste is fully incorporated into the coconut milk.
Bring the mixture to a gentle simmer. Allow it to cook for about 10-15 minutes, stirring occasionally.
Taste the curry and adjust the seasoning. Add lime juice for brightness and sugar if desired. Cook for an additional 2 minutes after adjustments.
Remove from heat and stir in chopped cilantro. Serve hot, garnished with extra cilantro, alongside jasmine rice or naan.