Pages 509 to 511 of the online PDF Manual state the following:
Tire Chains (Traction Devices)
Use of traction devices require sufficient tire-to-body clearance. Follow these recommendations to guard against damage.
Four Wheel Drive (4WD) Trailhawk Models:
The use of 9mm snow chains is permitted with the use of 225/65R17 tires on size 17 x 7.5 ET31 wheels.
Damage to Four Wheel Drive (4WD) Trailhawk Models may result if tire chain or traction devices are used with original equipment tires.
So for reference you should have OEM 245/65R17 tires on your TH. They are recommending that you cut down on the width of the tire by 20mm to allow for a 9mm diameter snow chain and still have 11mm of room to spare to maintain normal factory spec clearances.
So this of course all depends on the type of snow chain/cable you intend to use. There are other posts out there on manufacturers, however I looked at Thule and there are others too that are designed to not install on the interior sidewall of the tire and therefore you avoid the whole clearance issue from the get-go. Fair warning as they are a bit pricey.
Think of it this way, put bigger or wider tires on your car and you may have some rubbing or noise when you turn the wheel full deflection. Now think about how chains would rub on your wheelwells. NOT TOO GOOD!!! Don't turn your wheels fully and you're okay regardless.