Be aware that even if you hand-carry it to an Apple Genius Bar, they cannot fix it while you wait.
Removing the old battery requires nasty solvents that cannot be used or stored in a retail space without violating a litany of OSHA, HAZMAT, and fire codes. They send your computer to one of Apple's centralized repair/refurb centers. So you need to plan your service with your computer needs in mind. You may be without your computer for several days.
Even if you take it to an Apple Authorized Service Provider, they will have to ship it out.
Note that this service may not be available in all countries or regions. If you cannot have Apple do the service, buy a new computer. We see too many sad stories here from people who had a non-Apple battery service and ended up with a miserable aftermarket battery after paying big money.
It seems Apple makes an concerted effort to reduce turnaround time. Some of the senior contributors here report that when they had a laptop battery service, the laptop came back with not only with a new battery but a new or refurbed-to-new upper deck assembly with new keyboard and trackpad. That's a lot of work for the price.
