depends on a lot of factors, from what kind of chain, what kind of lube, where you ride, etc.
Just judging by the type of bike you have, I am guessing you are riding a combination of paved bike paths, sidewalks, neighborhood streets and packed gravel hike & bike trails, and you're not putting a ton of torque on it, riding creek crossings or in the rain or mud. I would also guess you have never lubed the chain, or if you have, maybe not with a legit bike chain lube.
If those assumptions are close to correct, then I'd say, yes the chain probably is ready to go at 1500 miles. No it's not likely to put the hurt on the chain rings or cassette since those are all steel and you are not riding real hard.
Now if you want to save money on chains in the long run, here's the routine: Buy a SRAM PC69 chain and a bottle of Rock & Roll Gold or other highish-end chain lube (Pedro's Ice Wax, maybe my favorite Maxima Chain Wax, etc.). Faithfully lube the new chain once a week or every 100 miles and you will probably get 3-5K out of the next chain. Invest in one of those chain cleaning machines from Pedro's or Park Tool and a bottle of Simple Green, and about every month or so (400-500 miles) clean the chain with the chain machine and Simple Green, then let it dry overnight and re-lube it. You'll get max life out of the chain and if you don't ride in the same gear all the time, probably sell the bike with the original cassette and chain rings still in working order.
If you neglect it, maybe replace it with a cheap chain and put WD-40 on it only when it has visible rust, then sooner rather than later it will start to ghost shift and skip and make noise and generally drive you nuts until you quit riding.