Heat the olive oil in a stock pot or a large skillet to high heat. Add the chicken and cook until chicken pieces are browned on both sides. Remove the chicken from the pan and set aside, keeping the remaining oil in the stock pot.
Add the onion and zucchini and saute until lightly browned. Add the garlic, curry powder, paprika, and salt and saute for 30 seconds.
Add the chicken back into the pot, along with the coconut milk. Bring to a boil.
Reduce heat to a simmer, cover the pot with a lid, and let simmer for 30 minutes, or until chicken is tender. Add the tomatoes to the pot in the last 5 minutes of cooking.
Serve in a bowl with the coconut broth, like a soup. Top with cilantro.