In a medium saucepan, heat the oil over medium. Add the bell pepper, onion, jalapeno and garlic. Season with salt and pepper and cook, stirring often, until the vegetables soften, about 5 minutes. Add the tomato paste, chili powder and cumin. Cook, stirring often, until fragrant, about 2 minutes. Stir in the tomatoes, chickpeas, black beans, pinto beans and 1/2 cup water and bring to a boil; reduce the heat to medium. Simmer, stirring occasionally, until the chili thickens, 20 to 25 minutes; season.
Divide the chili among bowls. Garnish with the sour cream and cilantro.