Step 1
Bring a large pot of salted water to a boil. Add pasta and cook, according to package directions, until al dente. Reserve 1 cup of the pasta cooking water, then drain the pasta.
Step 2
Meanwhile, in a large Dutch oven, heat the olive oil and chorizo over medium-high. Cook, stirring occasionally, until chorizo is crisp and brown, 2 to 3 minutes. Turn off the heat and use a slotted spoon to transfer the chorizo to a plate. Cook chickpeas for in remaining grease for 5 minutes and add to chorizo.
Step 3
Return the pot to medium heat and add the tomato paste and garlic. Cook, stirring, until the tomato paste is caramelized and a shade darker, 3 to 5 minutes, covering the pan if the splattering is wild. Add the red-pepper flakes and a few grinds of black pepper, then remove from heat.
Step 4
Add the cooked pasta and ½ cup of the reserved pasta water to the tomato mixture. Return the pot to the medium-high heat, and stir vigorously until the pasta is well coated. Add more pasta water until the sauce is glossy. Stir in the chorizo and chickpeas and season to taste with salt and pepper.