Typically the red LED comes on when the battery charge drops below a certain level. What is your battery gauge (or percentage, if you have that enabled) showing? If you have the battery fully charged, is it lasting a normal amount of time, or dying very quickly? If the latter, then there's likely something wrong with the battery (although there could be something wrong with the charging circuit in the phone).
Assuming that you don't have access to another battery, I'd do a Factory Reset just to eliminate any settings that you may have inadvertently changed (or any apps that may be causing the problem). If that doesn't fix the problem then it's time to take it in or call Customer Service.
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