Hey ZChi4Life!
I would try approaching them about a joint community service project or educational workshop. I'm sure we all share the similar goals when it comes community service and educating our community.
We did a lot of joint projects with other sororities. Most of the time, each org was planning on doing participating in the event anyways. Why not a joint effort!?!
Joint sorority functions work really well during Women's History Month. You can join forces to get really good speakers to come to campus and hold workshops, programs, panel discussions, poetry readings, etc.
Another surefire way: support them at their programs. Make sure a ZChi is there to represent and show Greek Unity. Believe me, they will reciprocate.
Having a party is another idea. However, I would hold off on a joint party until you have established some rapport with them. So, first work, then play!
Hope this helps!
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Sigma Lambda Upsilon: Sincerity, Loyalty, Unity
http://www.sigmalambdaupsilon.org