Heat the olive oil in a large pot over medium-high heat.
Add the onion, garlic, and ginger and sauté for 5 minutes, stirring occasionally.
Add the curry powder, cumin, and turmeric and stir to combine.
Pour in the coconut milk and vegetable broth and bring the mixture to a boil.
Reduce the heat to low and simmer for 20 minutes.
Stir in the chickpeas, rice, salt, and pepper and simmer for an additional 10 minutes.
Remove the soup from the heat and stir in the cilantro.
Serve the soup in bowls with a lime wedge on the side.