Just did a quick search and found this:

375 Winchester Brass for Reloading (50)

Not cheap - but it is available. There is also some available as loaded ammo on GB and other auction sites. I also read on another site that Winchester does do runs of this ammo on occasion. I'd give them a call and ask when. If you plan on shooting this rifle I would definitely set up for reloading of this caliber - I am a firm believer in getting what you need to be self sustaining while you can.