Heat olive oil in a large pot over medium heat. Add onions and cook until they soften, about 4-5 minutes.
Add garlic, half the uncooked corn, potatoes, celery, and carrots. Season with paprika, thyme, salt and pepper, and sautee until the vegetables soften, about 4-5 minutes.
Add vegetable broth and coconut milk. Bring mixture to a boil, then simmer until the potatoes are tender, about 15 minutes.
Use an immersion blender to blend the soup, or alternatively you could transfer the soup to a blender and blend that way.
Add the remaining uncooked corn to the pot. Return to a simmer to allow the corn to cook, about 10 minutes. Ladle the soup into bowls and serve with chives, if desired.