In a large pot, heat the olive oil over medium heat. Add the chopped onion and sauté until it becomes translucent, about 5 minutes.
Stir in the minced garlic and grated ginger, and cook for an additional minute until fragrant.
Add the diced chicken to the pot, seasoning it with salt, pepper, turmeric, cumin, and coriander. Cook until the chicken is no longer pink, about 5-7 minutes.
Pour in the chicken broth and coconut milk, stirring to combine. Bring the mixture to a simmer.
Add the diced carrot and zucchini to the pot. Let the soup simmer for 10-15 minutes until the vegetables are tender.
Stir in the baby spinach and cook for another 2-3 minutes until wilted.
Remove the pot from heat and squeeze in the lime juice. Adjust seasoning if necessary.