Heat oil in a large pot over medium heat. Add onion, garlic and bell pepper and saute for about 5 minutes until soft.
Add red curry paste, ginger and turmeric and stir until combined. Allow the spices to cook for 30 seconds, then add the broth, coconut milk, and shredded chicken.
Bring to a boil, then simmer uncovered for 35-40 minutes.
Ladle into bowls and add zucchini noodles. Top with cilantro and limes.