If you are looking for unity web player for chromebook, or any unity plugin for chromebook to play unity made games or apps, So here you should keep some answers in mind about chromebook from several people who already looking for this plugin.

Based on my research you cannot install any third party software or plugin into chromebook and unity web player is an additional plugin. :(

For your ease and saving you from searching lot more i collected some answers and comments regarding unity web player for chromebook

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Google product forum:


source:
https://productforums.google.com/forum/#!topic/chromebook-central/YSEaou6CgyY




Unity answers: 

0

Chrome OS does not support classical browser plug ins. It will, however, support Google native client at some point in the future, which we are also working on porting Unity to, so by publishing to NaCl, you will eventually have the option to run Unity web content on Chrome OS. more ▼ answered Sep 19, 2011 at 03:38 PM jonas echterhoff ♦♦ 10.6k ● 9 ● 41 ● 119

source:
http://answers.unity3d.com/questions/167512/unity-plugin-for-chromebook.html




Chromebookhq:

• • Y
• josh
  FEBRUARY 21, 2014 @ 10:53 PM
  how do i get the unity web player on my Chromebook ?
  REPLY
  • Ben
    MARCH 2, 2014 @ 2:39 AM
    The answer is you can’t. On Chrome os you can’t actually install anything so you can’t install unity in order to use it. ( Lot’s of people put game’s that run on unity on the chrome web store but you still can’t run them).

source:
http://www.chromebookhq.com/all-the-games-you-can-play-on-a-chromebook/