Heat a large pot or Dutch oven over medium-high heat. Add 1 tablespoon coconut oil. Once melted, add the onion, bell pepper, carrots, and green beans. Stir-fry for 6–8 minutes, stirring frequently, until the onions begin to soften but the beans and carrots are still slightly firm. Transfer vegetables to a large bowl and set aside.
Return the pan to the heat and add another tablespoon of coconut oil. Once melted, add the chicken and stir-fry for 6–7 minutes, stirring often, until mostly cooked through. (It’s okay if a few pink spots remain; the chicken will finish cooking in the soup.) Transfer chicken and any juices to the bowl with the vegetables.
Add the remaining tablespoon of coconut oil to the pan. Once melted, add the red curry paste and cook, stirring constantly, for 30 seconds until fragrant.
Return the chicken and vegetables to the pot. Cook for 1–2 minutes, stirring well, until evenly coated in the curry paste.
Add the coconut milk and chicken broth. Increase the heat to medium-high, bring the soup to a simmer, and cook uncovered for 5–6 minutes, until the green beans and carrots are tender.
Reduce the heat to low. Stir in the lime juice, agave syrup, and fish sauce until combined.
Serve hot, ladled over steamed rice or rice noodles. Garnish with cilantro and/or Thai basil, roasted peanuts, and lime wedges. Enjoy!