Here's a NASA-funded study from the early 2000s, arguing that a space elevator could be built as a paper-thin ribbon at least a meter wide, composed of carbon nanotubes 7cm long, bonded together with epoxy.
http://images.spaceref.com/docs/spaceelevator/521Edwards.pdf
The study also addresses lots of other engineering issues. This work sparked a lot of subsequent R&D that is still ongoing. We're not yet able to actually make the ribbon described in the study, but we're getting there.
Then again, if you're willing to rely on dynamic support, a minimal orbital ring could be built with materials we have today: