Is a C wire required to install this thermostat?

Yes, a C wire is required and is the primary power source for the thermostat. Without a C wire, the thermostat will not power up. If you don't have one, look for an unused wire pushed into the wall and connect it to the C terminal, verifying it connects to the 24 VAC common at your heating/cooling system. (Page 13)

From the official Honeywell RTH6580WF Wi-Fi Smart Thermostat manual, page 13

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