Is there any place to buy a replacement battery?

@albertemc2 there are no official replacement parts available for any Pixel. Looks like the battery is a Toshiba model. There is a company that is already shrouded in mystery, black helicopters and even more secretive than Apple. So it will be up to you to try and find one based on the actual battery. The Toshiba battery model is PA5280U-1BRS

Of course you can try places like this to see if they can match it.

Sears has this model posted. seems pretty spendy to me, if i were you I would look around a little more to see if i could find one cheaper, this one seems to be a little over 50.00 YIKES! there might be a way to rebuild your old battery.

http://www.sears.com/es/us/toshiba-pa520...

If you open the Crosh shell (Ctrl+Alt+T) I believe there is a command to test the battery's ability to hold a charge if you run `help_advanced` and look through the commands there.

Also keep in mind the screen brightness and the number of open tabs and the number of extensions you have running in the background can greatly affect your battery life.

I would run the above test once as your user, and then power off the Chromebook complete and boot fresh and rather than logging in again choose the "Guest" session, then use the same command you used in the Crosh shell and see whether the discharge rate is different.

You should also try running as Guest for a day or two and see if there is a large difference in battery life if you aren't logged in as your user with all your extensions/tabs/etc.

Let us know what the results are and we can give you more advice based on that information.