Here is an informal briefing on chance in literature -- personal communication from Jason Puskar.
18th Century fiction tends to be very interested in haphazard life stories. Sterne's absurdist novel Tristram Shandy is built around an accident that occurred at the hero's birth. Smollett's Roderick Random is more sentimental but flags its interest by its title. Road novels like Fielding's Joseph Andrews prefer haphazard one-thing-after-another plots, which minimize accounts of causation, rational agency, and over-arching structures. Turning to literary criticism, Thomas Kavanagh's book Enlightenment and the Shadows of Chance deals with, as its subtitle says, "The Novel and the Culture of Gambling in Eighteenth Century France".
There are a lot of novels in the 19th Century that start with accidents. A chance moment is really useful for starting a novel, because if something happens by chance, then there's (allegedly) no reason for it, and so no obligation on the part of the novelist or narrator to start any earlier. Austen's Sense and Sensibility, for instance, starts with a woman who falls and hurts her ankle, so that a man has to pick her up: the lovers get thrown together for no good reason, but because of that, the novel doesn't have to offer any other explanations. It can get on with what follows. Dickens is the famous novelist of coincidence, although he often tends to reveal chancy moments as somehow predestined or rational in the end. These novels of society seem to be chronicling, in one way or another, the surprising social connects that take place in modern cities and in increasingly mobile (socially, geographically) societies.
The most important body of fiction on chance is "naturalism", a variant of realism that's loosely indebted to Darwin, but also to various versions of scientific determinism. Stephen Crane (warfare), Joseph Conrad (who wrote a novel Chance), Jack London (physical calamities), Frank Norris (futures markets), Thomas Hardy, Emile Zola, and others, tend to stock their novels with outrageous and usually violent accidents. In some but not all cases, chance seems to indicate not much more than human ignorance of the invisible workings of a mechanical universe, but in others, especially Crane, the matter can be more complex.
Subsequent modernist fiction tends to romanticize chance, or mystify it, or psychologize it as a mental attitude. But Wallace Stevens's poetry is obsessed with directionless change; so, in a sense, is the music of Charles Ives. Both of those two worked in the insurance industry for their day jobs, which I find particularly interesting. Quite a few avant-garde artists were interested in chance: Tristan Tzara, Andre Breton, F.T. Marinetti, Stephan Mallarme.
Postmodern fiction is obsessed with the concept of chance, and is sometimes defined as a genre in which accounts of both structure and agency give way to the random play of chance. Thomas Pynchon's Gravity's Rainbow (with its interest in Poincare); Don Delillo's "airborn toxic event" in White Noise; William Gaddis's financial speculation in JR; Paul Auster's The Music of Chance; Lyn Hejinian's poetry (especially a volume called Happily); and many, many others. Post-structuralist philosophers, especially deconstructionists, have gravitated toward chance for similar reasons. See Derrida's essay "Mes Chances/My Chances" in Taking Chances: Derrida, Psychoanalysis, and Literature.