Well, part of ECC support is in the CPU itself since that's where the actual memory controller is. In addition, the motherboard has to support the ECC memory too. In general, if the motherboard specs on the Gigabyte website don't explicitly say 'Supports ECC RDIMMs' then it won't, regardless of what the CPU might support. In addition, only Xeon CPUs support ECC RAM.
So - looking at the spec sheet and support list: It does NOT list support for ECC - it supports non-ECC only. It does support Xeon CPUs, but since it only supports the non-ECC RAM, you can't use ECC RDIMMs with it.
Just as a quick note, usually ECC support these days is limited to either Server class or Workstation class motherboards. Your typical consumer level board doesn't support it. It used to be that they did - in fact I have a Gigabyte consumer board (high end at the time, but still consumer) with ECC/nonECC support running an Opteron 1354 QC (Socket AM2). It's somewhat of a shame that they've eliminated ECC from consumer level boards as there are some small businesses (like mine) which prefer the consistency and security of ECC for file servers and such.