I think most 100% linen is washable. Blends of linen and other fibers are another matter. If the skirt is lined, you may run the risk of having the lining or the linen shrink and the inside/outside not match each other any longer. If the lining is acetate, that stuff shrinks like crazy.

Use a mild soap, not a regular detergent. Don't wring. Roll it up in a towel and press the excess moisture out.
Lay it flat to dry. Iron it with a pressing cloth while still damp. I read someplace not to use vinegar on linen. To get the stain out, I'd let it soak in cold water with your mild detergent for several hours.

Another thing you might try is to use a powder dry cleaning product like Goddards or K2R. If it is a grease type stain from a sauteed chicken breast landing in your lap without your knowledge, this type product might help. Spray it on, leave it there for several days and take it back in for dry cleaning. I do this with any meal misshaps on my dry clean clothes when I get home. It soaks up any grease and works on the stain until I get it into the cleaners.

Thanks Barnmom! Would Woolite be fine to use? The skirt, which is 100% linen, is lined, and I believe it is an acetate lining. I didn't think acetate shrunk- thought it was like polyester. I will try the Woolite. I seriously doubt it is a grease stain, but again, I'm quite confused about the stain in general, as it wasn't there when I dropped it off at the dry cleaning.

If the lining is acetate, don't wash it. It is likely to shrink a lot. It is not like polyester. If you can snip a long slice from the seam of the lining, use it to check for shrinkage. Trace an outline of it and then wash it, dry it and iron it. Then place it on the ouline to see if it is the same size or not. Some acetates might be washable.

Woolite would be fine.