Like others have said, the markings look like they've resulted from the chain scratching the chainstay. This is not uncommon, and protecting the frame with some type of tape is the easiest and the most common solution. Mountain bikes, where this problem is more pronounced, often have very sturdy chain stay protectors (and a clutch mechanism in the rear derailleur to reduce the chain movement).
That said, you can also do a quick check that your drivetrain setup does not contribute to the issue. Switch to the smaller chainring in the front (assuming you have a two-by system) and to the smallest rear cog. The rear derailleur should be able to take all chain slack, i.e. the chain should feel taut, like in any other gear. If this is not the case and there is slack in the chain, your chain might be too long. If the chain is not too long, it is possible to adjust the rear derailleur to keep the chain more taut. (Also, it's not recommended to cross-chain like that; if you have a two-by system and you often ride with the small chainring and a small sprocket, try to make a habit to switch to the larger chainring earlier.)
Checking the chain length and/or adjusting the B screw is not hard. Your rear derailleur manual should explain the process, but here is an example of one Shimano manual. Page 12 explains how to measure the chain length (note that you have to remove the chain, so this is way easier if you have a quick link in your chain). Page 17 explains how to adjust the "end adjust bolt" (aka B-tension screw), mentioning its use to remove the slack.
You mentioned your bike is new. If there's any slack in the chain, it should get fixed in warranty/as a part of the first maintenance. On the other hand, even if the main cause is too long chain, the protective tape will help keeping the frame in better condition and it will protect the chainstay also when the chain is dropped so you might want to consider it in any case.