Does anyone have experience running Z chains on 315-35-R20 tires?

I want to take my 2013 M sport up to the mountains and want chains if it gets really icy or deep snow. It appears I have enough clearance around the tire but would like to hear of any firsthand experience. I like the low profile cable Z chains. I've looked into "tire socks" but they don't look very impressive. Thanks in advance for any advice.

__________________
2013 X5 3.5i M Sport
2004 M3 cabriolet SMG