I don’t use Facebook nor Chrome for the very reasons this project advocates, so cannot put it to the test myself, but Data Selfie by Hang Do Thi Duc and Regina Flores Mir looks like a great tool to bring closer to the user just how much social network providers know about them:
Data Selfie is a browser extension that tracks you while you are on Facebook to show you your own data traces and reveal how machine learning algorithms use your data to gain insights about your personality.
The tool explores our relationship to the online data we leave behind as a result of media consumption and social networks - the information you share consciously and unconsciously.
Here is how it works (if you prefer not to view embedded videos, watch it at Vimeo):
PS: FastCoDesign has a comprehensive write-up on the project as well.