If by "real crystal" you mean cut quartz rock, as in gem stone, it would be very VERY unlikely that you or anyone even the Russian Tzars would have a chandeliere with cut gem stones as prisms.
Crystal is cut glass....or not!...Crystal may be blown and not cut....crystal may be pressed glass. The term "crystal" usually denotes glass with a high lead content....and I have never seen nor heard of glass being cut that is not of a high lead content.
However I have seen inexpensive chandelieres with prizms that are molded and not cut.
If the chandeliere was original to the house you are leaving, I would leave it with the house.
Linda C

Thanks but no, I didn't mean quartz rock...I realize that isn't used...I guess I should have stated lead crystal or glass. We are in the desert and I've never seen a chandelier in anyone's house here..it's too dusty and dirty and why we took it down.

They make something called "Chandeliere cleaner"....you simply spray it on the chandeliere, put newspapers underneath to catch the drips and presto! a clean chandeliere.
I have seen more than a few crystal chandelieres in the Phoenix area.

Here is a link that might be useful: cleaner

Try blowing it with hairdryer if the dust is not too attached or use a solution of water and white vinegar

Here is a link that might be useful: Crystal Chandeliers

If it were original to the house, it likely has little to no antique value and you could find styles nearly identical in stores today. Is the issue that it may be a valuable piece because the prisms are crystal, as opposed to glass? IOW, you'd only save it if they were real crystal?

Look at the other materials in this fixture to determine if it's a fine, arty piece worth keeping or not. I got a crystal hurricane lamp a few years ago at the supermarket for eight dollars, so crystal itself doesn't necessary imply quality, just glass with lead in it. On the other hand, I bought a chandelier at a hardware store with plain old glass prisms on it and I paid a small fortune for it even at half price. See what I mean?

BTW, regarding that chandelier from the hardware store.........I hung it in my kitchen at my farm house and filthy it got from horse dust and gas grease! The easiest way I found to clean the scads of prisms was to just unhook them and run them though my dishwasher. LOL.

Most likely, it's vintage, but not antique. Most chandelier crystals are merely glass, molded. Also, if the arms are molded, with noticeable seams, it's modern. Check out a few lighting sites, and see if there is a chandelier similar to yours. If so, you should be able to base your decision on that.