Hi there,
This sounds like you might have a bad connection between the phone and the charger. Is there any chance the phone has been dropped while connected to the charger or could the microUSB port on the phone have been damaged in any way? If the phone is still under warranty, I would recommend taking it to your carrier for assistance.
If it's no longer under warranty, see if another charger will work. If it does, then the charger may be damaged at or around the connection to the phone. If you still have the problem with a new charger, then it's likely the phone that's the problem. If you don't have access to another charger, try simply using the USB cable and plug it into your computer. That will work as well.
If the problem is narrowed down to the phone, take a look at the microUSB port. Does it look damaged or dirty at all? Is it lose?
Let us know how it goes and good luck!. 
