If it's something against the law, and your Delta Zeta chapter's reputation could be at stake, you MUST approach the President who will deal with it on a J-Board level. If it's about ritual, you need to take her aside and talk it out with her and find out why she felt the need to reveal and tell her if she can't pull it together, you are going to have to talk to the President about it. College is supposed to be about being adults and taking responsibility for your own actions, and she needs to deal with what she did wrong.
Achtung, if you want to talk about it with me offlist, I can certainly help you out more. I won't reveal anything, besides, I don't know what chapter you are from anyway.
If this sister's conduct is unbecoming of a Delta Zeta in a big way, it is a big deal. I think you already know that what she has done is wrong, or you wouldn't be posting here about it. It's up to you and your conscious to decide how to handle it, but I can certainly give you some advice from an Alumnae Leader standpoint.

Tracy