Your Greek sorority pin is Beta Delta Phi, which is a sorority at Sacred Heart University in Connecticut. SHU is Catholic university that was established in 1963. I couldn't find any other college or university where Beta Delta Phi was a national sorority.
I think this sorority pin is probably from the 1970's judging by how it is made and by the fact that SHU was established in 1963. This pin is made almost identical to my Sigma Sigma Sigma sorority pin, which is black onyx surrounded by pearls and set in 10K gold. Mine also has a 'guard' located on the end of the chain. Guard chains were usually on sorority pins of Officers.
In my sorority, the sorority pin was very sacred and was to be buried with the owner or returned to the National order. The Greek loyalist were/are trying to keep the sorority pins out of the hands on non-member, thus the price has skyrocketed.
Turbo21, I didn't want to overwhelm you with information in my first post, but now that Breezie has given a bit of introduction from "those in the know", I feel a bit more comfortable giving additional information for you to consider.
In an internet search, I also found the sorority posted by Breezie, however, that sorority was very small and no longer exists. I'm not convinced that it existed for very long or that it was a "national" sorority (i.e., existed at any other university). That's not to say that it can't be from that particular sorority -- just that there is a very narrow window of time and geographic space where that would have made sense. Now, there are a lot of other issues to consider here:
1. While unlikely, the pin may not be from a sorority, but rather, a fraternity. The only case where this makes sense of course is if this is what is known as a "sweetheart pin", i.e., a special type of pin that is purchased to give to one's female significant other instead of one of more personal significance (e.g., one's "pledge pin"). Again this is unlikely, but something worth considering.
As an example, there was a fraternity at the University of Minnesota with those letters in the 1920s.
2. This pin may not be from a sorority or a fraternity, but a collegiate national honors society. Fraternities and sororities are not the only organizations which use Greek letter dyad/triads. College level honor societies, usually focused on specific majors/disciplines, also use them and often have their own apparel/memorabilia/regalia. As an example,
as recently as 2013 there was a biology honors society with the letters "ΒΔΦ", as can be seen in this Queens College newsletter pdf.
3. As mentioned before, this may be from a one-off, local sorority. This would make it very difficult to trace the organization, especially if it is now defunct. As an example,
there is a one-off fraternity at Iowa State University called "Adelante".
4. The letters on this pin may signify a "fraternity within a fraternity" or a "sorority within a sorority", and be virtually untraceable except if recognized by a member of the parent Greek organization. Many sororities and fraternities have internal, special "orders" with their own Greek letters for which one's membership represents a special achievement or position within the fraternity or sorority. These are usually regarded as "secret" and known only to the members, but often come with special pins and certificates awarded to the qualifying individual.
5. Finally, the letter attached by the chain could prove useful in identifying the pin's geographic origin or owner. While the letter attachment can range in meaning from completely personal (chosen by the owner from hundreds of charms) to broad and generic (all owners got the same charm), a letter sometimes signifies either the chapter of the sorority/fraternity (in this case, "Iota", if I'm seeing it correctly) or the name of the owner (e.g., "Irene"). It could also be meaningless, or combined with the shape of the main pin, meant to signify "I ♥ ΒΔΦ".
If you want to be sure of the ID of this piece, a good place to start would be by contacting the Greek Affairs office at Sacred Heart University and seeing if they can put you in contact with an alum of ΒΔΦ or some individual otherwise familiar with it.
-mcl