Heat the oil in a large skillet over medium-high heat. Add the onion and cook until soft and translucent, about 3 minutes. Add the carrot, zucchini, and garlic and cook, stirring, until the carrots are firm-tender, 4 to 5 minutes. Add the tomato paste, stirring to incorporate completely. Add the chicken broth and chickpeas and bring to a boil. Reduce the heat to low and cook, covered, until the liquid thickens slightly, 8 to 10 minutes.