I have had 4 Chase cards at once acquired over the course of a year. The general consensus is you can get approved for 1 Chase card every 30 days; 2 at once is rare and requires a phone call to Chase. Chase has so many good rewards cards I wouldn't want to get on their blacklist.

Decide which Chase card you want first, make extra sure it has been a minimum of 30 days, and apply. Save the second card for later.