Bring a large pot of lightly salted water to a boil. Cook spaghetti in the boiling water, stirring occasionally, until tender yet firm to the bite, about 12 minutes. Drain, reserving about 1 cup of cooking water.
Heat olive oil in a large skillet over medium heat and cook garlic until fragrant, about 1 minute. Add kale and cook, stirring constantly, until wilted, about 3 minutes.
Stir cooked spaghetti into the skillet. Add nutritional yeast. Add enough of the reserved cooking water to create a thick sauce. Stir well. Add chickpeas and heat until warmed, 2 to 4 minutes. Season with salt and pepper.