MBP first generation Service Battery My MacBook Pro is throwing me a message "Service Battery" and coconutBattery tells me I have 4007 mAh instead of 5450 mAh.

Is there a way to pump it back up or is that impossible?

I was looking around on the Internet but the Apple Store does not display a built-in MacBook Pro 13 inch battery.

Should I replace mine? And if so, where is the best place to look for since Apple does not have them theirselves?
Battery degradation is normal, and seeing that your battery is almost 4 years old has went through 820 cycles, you battery retention is still quite good. Degradation of battery is irreversible.

If you really want to get a fresh battery, you can take it to an Apple store. It'll cost somewhere around $150.

Apple replace defective notebook battery only within 3 years of purchase with AppleCare, so you wouldn't get that benefit.