Chrome: Fly Photo Editor sends photos straight from Facebook to the web-based photo editor Aviary, so you can touch them up before sharing them with friends.
To open up the editor, just hover over any photo in Facebook and click the "Fly Editor" option below the image. The photo will instantly load up in the Aviary-powered Fly Photo Editor, where you can make the usual adjustments to brightness, contrast and saturation, or even some advanced edits like tilt-shift style focus or colour splashes.
Once you're satisfied, Fly Photo Editor will upload the photo back to Facebook and share it on your timeline. Unfortunately, the only exporting option is to send the photo back to your Facebook wall, but you can save it from there to archive locally or share on other social networks. This is far from the most advanced photo editing option available, but it's certainly quick and easy if you keep a lot of pictures on Facebook.