Yes - you will need chains by law in the car.
https://www.autostrade.it/en/la-nost...ioni-invernali
Typically, the rental car company provides them, sometimes free sometimes at a charge, check your contract to see which is the case.

Your Chase Sapphire Reserve card provides primary coverage when in Italy. I have the same card and specifically acquired it for rentals in Italy. In fact, I have a reservation with Hertz via AutoEurope @ MXP late February and it's on that card.

I would look very carefully at the insurance on the rental. If the $35 is for the mandatory insurance (by law in Italy you are forced to take the mandatory "basic" coverage), it still leaves a large deductible (you should check the deductibles) and you can't decline it. You can buy a "Zero Coverage" rider but it tends to be expensive. Alternatively, use your Chase Sapphire Reserve card for incremental coverage. Just be careful as you MUST decline any optional coverage. If you accept any, either in advance or when you pick up the car, you will lose coverage from the card. You should take documentation that shows the card provides coverage to show them at the agency if needed (although I've never had any problem with Hertz - it's the minor agencies that are pushing rental riders that can be difficult.