Google Chrome Extension - Script Injections

In addition to the answers above I notice that in your contentscript.js you are just adding another script i.e script.js Why don't you directly add script.js through content_scripts in manifest.json.

1. In your manifest file, "manifest_version": 2 is specified. This automatically activates a stricter mode, in which all extension's files are not available to web pages by default.
2. Your original code would never work, because the <script> element is immediately removed after injection (the script file does not have a chance to load).

As a result of 1., the following error shows up in the console:

Failed to load resource                             chrome-extension://invalid/

To fix the problem, add script.js to the whitelist, "web_accessible_resources" in your manifest file:

{
  "name": "Chrome Extension",
  "version": "1.0",
  "manifest_version": 2,
  "content_scripts": [{
      "matches": ["http://pagetoinject/script/into/*"],
      "js": ["contentscript.js"]
  }],
  "web_accessible_resources": ["script.js"]
}