I turned on my Fire TV stick and saw a message on the homepage for a free $10 prime video credit that can be used on video rentals or purchases. Just click through to redeem (it required me to re-sign into my Amazon account). Credit expires Feb. 15. I would assume the same is available if you own a Fire TV box or cube. See Screenshots of my TV attached.
Update: since not everyone's getting it, it appears to be targeted.