Android Central have reported that Audible areworking on an Android app. It's still in beta, though. To get the app you need to join the Audible for Android Beta Google Group.
The app links to your Audible account and allows you to download and listen to any audiobooks purchased through that account. One of it's neat features is that you don’t have to wait for the full download before you listen to the audiobook. Sideloading (over USB) is also supported.