What to do here on Linux is a bit more complicated; as Ben observes, you really want to behave how the window manager expects, but appeasing the couple of different Windows window managers is a different problem than the wide variety found on Linuxes. Custom theming also complicates things -- the Chromium colors were carefully chosen to look good alongside the rest of Windows but they'll likely not go with Ubuntu brown.
The options as I see them are:
- Make something that looks like Chromium on Windows, perhaps attempting to feed in the color of the window frame from the system.
- Give it a normal title bar, but try shoving the tabs up flush with it. Sounds ugly, but both of these options sound ugly to me.
More fundamentally, a majority of the developers working on the Linux bits use tiling window managers anyway, which in some sense obviate the whole idea of tabs on top. From the user experience docs: "In the long term, we think of Chromium as a tabbed window manager or shell for the web rather than a browser application."