Try dampening the area with a cloth and hitting it with a hair dryer as you go.

After the wedding, I washed DD's wedding gown - skirt only - in the bathtub. A line was left on the silk underskirt. A Google search showed that that will sometimes happen if two areas of the fabric dry differently. I dampened the area of the line and dried it with a hair dryer as I went. The line disappeared. YMMV but you have little to lose.

Thanks bbstx, I'll try that right now.

Try Folex; I swear that stuff works miracles. The only places I can find it is Home Depot and Bed Bath and Beyond. Comes in a white spray bottle.

Folex is my go to solution for stains, too, but I haven't found it to work on water marked fabric. Looking forward to hearing whether bbstx's suggestion works. Lowes also carries Folex.

Folex does not work well on water marked fabric. Ask me how I know. :(

I have found that many water marks are actually an accumulation of dirt. If you don't have anything to lose, I would upholstery clean the entire chair and see how that works. I have a commercial one that I actually use TIDE detergent with, and I have had very very good luck removing stains. But again, it could ruin the entire chair so make sure you are willing to gamble on it. Good luck!