In short, yes. The battery charges inside the camera using an included USB cable. The cable may be connected to your computer's USB port for charging or connected to the included AC adapter to plug into a wall outlet.
The battery is charged in place in the camera via a cord that is plugged into an electrical outlet. Like a cell phone, there is no separate external charger as charging is done while the battery remains inside the device.
The camera is the charger. It's annoying so I would suggest buying a battery charger so that you can continue to use your camera while simultaneously charging a battery. (assuming you purchase additional batteries, which I highly recommend) The usb cable to charge the battery is super short too, also annoying. This camera definitely has some downfalls compared to the older models of Olympus Tough that are no longer made but it does take great photos.