Do you want the entire thing to be clear, or can the ends be a metal?

The rod for sure. Either or about the posts. Do you know where I can purchase one?

A brand called Ginger makes some very pretty ones!
Some showrooms will have them and so does their website and numerous other places. They make the best looking ones, at least to me.

Here is a link that might be useful: {{gwi:2132983}}

I Googled and got a whole page of possibilities.

-Babka

Here is a link that might be useful: Lucite or acrylic towel bars

Restoration Hardware has a few. (They might be glass, but same look.)

I also like the look of lucite towel bars. I bought one at a yard sale that is very similar to the Ginger double bar, but it was shorter than I wanted, so I ordered a long clear acrylic bar (1-inch diameter, in this case) on eBay, and DH cut it to the appropriate lengths with a hacksaw. The original rods were not glued in, and the new rack was easy to install.