In a large pot, heat the olive oil over medium heat. Add the chopped onion and sauté until translucent, about 5 minutes.
Stir in the minced garlic and ginger, cooking for an additional minute until fragrant.
Add the diced chicken thighs to the pot and season with turmeric, cumin, black pepper, and cayenne pepper. Cook the chicken until browned on all sides, about 5-7 minutes.
Toss in the diced carrots and celery, stirring to combine. Cook for another 3-4 minutes to soften the vegetables.
Pour in the chicken broth, bringing the mixture to a boil. Once boiling, reduce the heat to a simmer and cook for 15-20 minutes, allowing the flavors to meld.
Stir in the coconut milk and kale, and cook for an additional 5 minutes until the kale is wilted and tender.
Remove the soup from heat and stir in fresh lime juice. Adjust seasoning with salt and additional lime juice if desired.