Putting a towel on the chair can be helpful. I use one made of microfiber as it works best for me. Microfiber is especially good at absorbing moisture from both sides, and is often used in sportswear to wick away perspiration.
I recommend it for your application because keeping your chair dry can help it feel cooler. If you're worried about appearance, microfiber's very thin, and can go unnoticed by co-workers. Even if they see the towel, it tends to be fairly unobtrusive. Since it comes in many colors, you can choose something that closely matches your chair. The material is easy to cut, and doesn't easily fray, so you can size it as you see fit.
I keep a number of these towels around the house, as they're good for many things. If you don't happen to have any, they're inexpensive (at least here in Northeast United States), and can be found at a variety of stores. Best of all, they wash easily and last a very long time.