Heat the oven to 425 °F. Rinse and drain the chickpeas, spread them on a clean kitchen towel and rub until completely dry; wet chickpeas steam instead of crisping.
Tip the dry chickpeas onto a rimmed baking sheet in a single layer, add the olive oil, salt and pepper, and toss to coat.
Roast 25-30 minutes, shaking the pan at the 15-minute mark, until the chickpeas are crisp, dry and some have split open.
While they roast, stir together the chili powder, smoked paprika, garlic powder and lime zest in a small bowl.
Sprinkle the spice mix over the hot chickpeas, toss on the sheet and return to the oven for 3 minutes to set the spices.
Slide into a serving bowl, squeeze the lime juice over just before serving and eat while warm; they soften after about 2 hours, so dress them close to party time.