This took me longer than it should, so here are the steps:

  1. Go to https://developer.apple.com/downloads/

  2. Search for “Graphics Tools” (searching for “Quartz” yields zero results)

  3. Click the + icon next to version of Xcode you are running (“Graphics Tools for Xcode 6.3”)

  4. Open the downloaded .dmg and then drag Quartz Composer.app into your Applications directory