There’s a large chain store in my area that is trying to close down a new competing store by selling their products at below market prices.
Is it permissible to buy at this chain store?
Assuming that the new store is local, the lowering of price by the chain store is not legitimate in halachah, because the local store will not be able to compete, and will therefore go out of business.
This halachah is based on the opinion of the Aviasaf, which is mentioned by the Rema, and cited by the Chasam Sofer and others.
Although there is no formal prohibition to buy at the chain store, it is therefore better to avoid buying there.
This answer assumes that both stores are of Jewish ownership, and that there is a large enough market for both to operate in competition with one another.