Heat olive oil in a pot over medium heat and cook onion until soft and translucent, about 5 minutes. Add garlic and cook until fragrant, about 30 seconds. Add potato and cook for 3 to 5 minutes. Stir in lentils. Pour in vegetable broth and simmer for 20 minutes. Add kidney beans, corn, and tomato puree. Bring to a boil; reduce heat, cover, and simmer until flavors combine, about 10 minutes. Season with paprika, chili powder, salt, pepper, and sugar.
Divide chili among 4 bowls and sprinkle with chives.