The Fighting Chance (1906) is another society romance by Robert Chambers, intentionally written in the same vein as the other "popular phrase" series, such as The Danger Mark and The Firing Line. (These were all popular phrases, honest!)
The central plot, as with these other two, is a somewhat-star-crossed romance. Boy meets girl, boy loses girl, boy is thrown out of exclusive New York clubs and takes to drink, boy finds girl again. In the course of meeting/losing/finding, the boy and girl in question both reveal their shameful inner weaknesses and, eventually, come to the conclusion that they should marry regardless. There's not a lot of mystery in what will happen, merely in how it comes about.
In The Fighting Chance, the romantic core of the book is provided by Stephen Siward and Sylvia Landis. The two meet in the first pages of the book, fall in love in the first few chapters, and spend the rest of the 400-odd pages trying desperately to keep one another at arm's length (and ultimately failing to do so).