The battery is located down in the right fender. You first remove the louvered plastic wheel house panel - good luck getting it off! The screw clips go flying all over when you try to wrestle it off from the rest of the plastic wheel house. Then remove the air cleaner housing by removing the intake hose from it and then pulling up on it then to the left of the car. Now disconnect the one exposed battery terminal. BE VERY CAREFUL, as I recall, all that you have access to is the Positive terminal. Disconnecting the positive terminal first is dangerous, you should always disconnect the negative first but it isn't accessible until you slide the battery halfway out the right front wheel well. Then remove the battery hold down. NOW you can finally slide the battery aft through the access hole in the wheel well. In order to slide the battery out, the front tires must be turned all the way to either the left or the right, sorry but I forget which way. Finally, disconnect the other battery terminal and remove it down and out of the wheel well.
The procedure described above is for a Chrysler 300M. The question specifically asked for instructions how to remove the battery in a 300C.
Read more: http://wiki.answers.com/Q/How_do_you_remove_the_battery_for_a_Chrysler_300C#ixzz1OQb1dmLM
