I didn't. But it seems he did: The Whole Family: A Novel by Twelve Authors (1908) includes a chapter by Henry James -- Chapter 7, "The Married Son". I wouldn't have guessed it.
(A round-robin story is a story written by multiple authors -- essentially a stunt, although there have been a fair number of them.)
Aside from James, the other author involved who's still read today is William Dean Howells, who wrote the first chapter, "The Father" (and seems to have conceived of the whole project). I haven't read it, but if you want to, you can find the book on Gutenberg. (Aside from Howells and James, the authors are, today, mostly forgotten.)
In other Jamesiana, Alice James, the diarist and sister of novelist Henry and philosopher & psychologist William, was born on August 7, 1848. This wouldn't be worth mentioning save that a surprising number of web sites -- PBS, and the "about" page for the publisher Alice James Books are two -- list her as born in 1850. I'm not sure how this alternative date got started. I'm pretty sure it's wrong, although both are quite prominently listed. (One telling fact is that the specific day is always associated with the year 1848.) Does anyone have any information on this? (To confuse things further, Alice was also the name of William James's wife; she was born 1849.)
Update: While I'm sharing stray oddities about the James siblings, I'll mention one more, which isn't widely known (although Louis Menand talks about it in his fabulous book The Metaphysical Club), which is that the third child of Henry James Sr. (after philosopher William and novelist Henry (Jr), but before diarist Alice) was Garth Wilkinson James -- called Wilky James -- who was one of the (white) officers in the (all-black infantry) 54th Massachusetts Regiment in the Civil War -- the regiment whose formation and attack on Fort Wagner is depicted in the movie Glory. Wilky James was wounded in the attack on Fort Wagner, and never fully recovered, suffering from various pains and ailments until his death at age 38.