I nominate The Good Earth
by Pearl S Buck. It's a modern classic as it was first published in 1930.
It only recently became available in ebook form for the first time and is also available in some libraries through Overdrive.
Amazon (US): http://www.amazon.com/The-Good-Earth...the+good+earth
Amazon (UK): http://www.amazon.co.uk/The-Good-Ear...3420155&sr=1-1
The Good Earth is a novel by Pearl S. Buck published in 1931 and awarded the Pulitzer Prize for the Novel in 1932. The best-selling novel in the United States in both 1931 and 1932, it was an influential factor in Buck's winning the Nobel Prize for Literature in 1938. It is the first book in a trilogy that includes Sons (1932) and A House Divided (1935).
The novel of family life in a Chinese village before World War II has been a steady favorite ever since. In 2004, the book was returned to the bestseller list when chosen by the television host Oprah Winfrey for Oprah's Book Club. The novel helped prepare Americans of the 1930s to consider Chinese as allies in the coming war with Japan.
A Broadway stage adaptation was produced by the Theatre Guild in 1932, written by the father and son playwriting team of Owen and Donald Davis, but it was poorly received by the critics, and ran only 56 performances. However, the 1937 film, The Good Earth, which was based on the stage version, was more successful.
I don't know if 1931 constitutes classic - more a modern classic I guess. But I'll let nominations/voting take care of that.