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Hmm, I guess there would be three options:

  • Compile Qt for Google Native Client and then compile Tiled against that version of Qt, in order to eventually have something that you may be able to distribute to Chrome browsers. Not an easy project and making Tiled usable in that environment will likely require additional changes.
  • Install a Linux desktop alongside Chrome OS, so you can install Tiled there. Note this should not be read as a recommendation to do it.
  • Use a remote desktop application to access Tiled installed on another computer.