The camera LED on my OnePlus One is continuously on I recently got a OnePlus One phone (64GB model). I noticed that the LED for the front camera is continuously on. Is there any option to turn it off?
When you say LED for the front camera, do you mean the notification LED? That can be easily disabled in Settings - Display and Lights - Notification and Battery light. 
If you're referring to the flash LED of the back camera, you can try taking some pictures with the flash turned off and see whether it works. 
If not, try hard reset via recovery.