Exciting news from the KiCad blog:
As a preview of a feature coming in the next major release, the ability to import Altium PcbDoc files is now available in the latest nightly builds. This was thanks to the work of Thomas Pointhuber in MR#60
The board import option can be found under the File > Import Non-Kicad Board File option and changing the file type filter
After selecting your PcbDoc file and a short delay. Pcbnew will display it’s best attempt at a import and provide warnings if it had any difficulties importing the file.
If you want to give the board import a spin, simply download the latest KiCad nightly and take it for a spin. Feel free to report any issues.
Both this feature and nightly builds are in development, please only use them for testing and experimentation