You may be better off getting a Raspberry Pi 3. It's a few more dollars but has way bigger user base, software support and features. The C.H.I.P. claims to be $9 and that is a good selling feature, but really at this end of the spectrum, anything under $50 that is going to be supported long enough and may let you try some development as well may be more useful. If you plan on video and graphics or gaming, or want tons of tutorials and a huge knowledge base for getting things done, RasPi will beat CHIP.
As far as powering either one, how are you planning to get 5V from the TV at high enough current? Keep in mind you also have a keyboard, mouse, and may want to plug in other USB peripherals. If using the USB port, I'm not sure if it will handle the power draw. You need to check what average power CHIP or RasPi use with added peripherals. I would use a higher end smartphone or tablet charger, usually they are up near 2.0 A. If you are worried about hiding the wires, you can run a single cord from the mains outlet to the back of the TV and then split it off there.