split aces

Hi, Just a quick question, I'm quite new to the game, and was just wondering, I'm playing at a table which does NOT allow you to hit split Aces (as well as not being able to double soft hands), should I still split if I get a pair of Aces? I'm not sure if this is a common rule or not since...

I am seeking what the odds are of a very, very unusual blackjack hand!!! Ready for this scenario?? A six deck blackjack table. (standard blackjack.) A player is dealt two aces (A1 & A2). She splits. A1 is dealt an ace (A3) - so she splits again. A1 is dealt an ace (A4) - so she splits again...