Battery is included, a designated battery charger is not. The camera comes with a plug in USB travel adapter and cable, which will allow the battery to be charged in camera.
I would recommend the purchase of an additional battery so you have a charged replacement. If you feel you need a stand alone charger, there are some nice travel chargers out there that can accommodate both AC and your cars DC charging, allowing you to charge a spare at home, in a hotel room or on the road.