Well, let's have a look at the boards:
Big picture of the GA-965p-DS3:
http://www.gigabyte.com.tw/FileList/Ima ... s3_big.jpg
DFi Infinity 975X-G (my own board):
http://us.dfi.com.tw/Upload/Product_Pic ... 975X-G.jpg
As you can see, the chipset cooler on the Gigabyte board is almost *exactly* as far away from the silkscreened CPU cooler area on the motherboard as it is on my DFi board. You also have to remember that the HR-05 itself isn't as wide as the stock cooler - it's very narrow side-to-side, while being longer front-to-back, as you're looking at the chipset from the direction of the DIMMs.
As you can see from a pic from my own PC (http://www.benslie.clara.co.uk/pc/2.JPG
), the HR-05 fits next to the ninja with absolutely no problems (nowhere near touching), so I'm gonna say it really will fit on the Gigabyte board with no problem at all =).