Heat the olive oil in a large pot over medium heat. Add the onion, carrots, and red bell pepper. Cook for 4 minutes until the vegetables start to soften.
Stir in the garlic and ginger. Cook for 1 minute until fragrant.
Add the chicken pieces and cook for 5 minutes, stirring occasionally, until the chicken is no longer pink on the outside.
Mix in the Thai red curry paste and cook for 1 minute to toast the spices.
Pour in the chicken broth and light coconut milk. Bring the soup to a simmer and cook for 10 minutes.
Add the spinach and lime juice. Stir until the spinach wilts, about 2 minutes. Season with salt and black pepper.
Remove the pot from heat and stir in the chopped cilantro before serving.