Not until you find a Well of Charon. Wells of Charon will not spawn during your first run or in the first four chambers of Tartarus, though they will always be available in the stairway after each boss. Even then, you have to wait until six runs in before a Chaos Gate begins to spawn. Chaos Gates are more common in Tartarus, with their frequency decreasing as you progress through the levels. However, if you want to ensure that a Chaos Gate spawns in your next room, I recommend buying a Light of Ixion from a Well of Charon if one is available to you.