It should be possible but if you take a look at the hardware platforms supported by Contiki, there are no x86 SoCs so you would have to port everything of the OS to the architecture of Galileo. This is the link to the Contiki Community site, in there you should get more information on how to port their OS to other platforms.
Hi connor100 and JPMontero_Intel,
We just released a Contiki port for Intel Galileo board!
You are welcome to visit the repository  and share your feedback with us. In platform/galileo/README.md, you will find information about the currently-supported Contiki APIs and device drivers, as well as detailed instructions on how to build, run and debug applications for this platform.
We just announced the Galileo port to Contiki community  and we hope we'll get it integrated into Contiki mainline!