Costco doesn't deal with parts or repair. Return and exchange for a new unit, or if it's out of Costco's warranty period, contact the manufacturer for replacement parts.
Hi Heather, in order to return any item at Costco you must bring in the entire product. Like Craig mentioned above it you are only wanting to replace the belt that broke. I recommend you reach out to the manufacturer of the treadmill.
The whole thing
Make sure the whole unit is still under Costco for replacement or contact the manufacturer to find replacement belt.
I agree with all of the above answers Hope you get it replaced or a new belt
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