There are cheap apartments and then there are cheap apartments. We waded through the low-end listings in search of the latter and noticed that there is a heretofore unremarked battle of the cheap apartments raging in a corner of Chelsea. The battlefield: 101 West 23rd Street. The warriors: apartments 2O, 2N, and 6F, each vying to be the first to sell. The weapons: teeny tiny PriceChops. Unit #6F was the first to reduce its price, lopping off $25,000 last month for the current ask of $275,000. Unit #2O came next, with a 2 percent price cut 10 days ago for an ask of $273,500. So far unit #2N has stayed above the fray with an asking price of $289,000, but it appears to have been pulled off the market this summer after not selling at $300,000. Who will be the next to Chop?