Place the water, chickpeas, and salt in a 7-quart pressure cooker (the water should cover the chickpeas and come to the 1/3 full line). Cover and lock the lid. Bring to pressure over high heat, about 15 minutes.
Reduce the heat to low, so that you barely hear hissing from the pot. Cook for 45 minutes.
Release the pressure by running cold water over the lid for 5 minutes. Open carefully. Drain and serve immediately, or use in desired dish.