The Ascent of Mont Blanc by Albert Smith (1853) — Smith climbed Mont Blanc in 1851 and turned the experience into a theatrical one-man show that ran for six years in London's Egyptian Hall, introducing the Alps to a mass audience. His account of the climb is vivid and funny, and his descriptions of the valley and its guides are the best record we have of what Chamonix looked like in the mid-19th century.
Touching the Void by Joe Simpson (1988) — Not set in Chamonix, but the foundational text of modern mountain writing, and a book that changed the way climbers think about survival and moral obligation. If you are coming to Chamonix to climb, read this first. Simpson's later memoir The Beckoning Silence (2002) is directly about the Eiger and the history of its north face, visible from Chamonix on a clear day.
The Cruel Way by Ella Maillart (1947) — Maillart grew up in Geneva and became one of the 20th century's great adventurers, travelling overland to Afghanistan in 1939 with the writer Annemarie Schwarzenbach. She spent much of her life around the Alps and her writing captures the landscape with the precision of someone who knows mountains as home rather than destination.
Mont Blanc Massif: The 100 Finest Routes by Gaston Rébuffat (1973) — The classic guide to the range by one of its greatest climbers, with lyrical route descriptions that read as well as they function. Rébuffat was a member of the first team to climb Annapurna and his Chamonix knowledge was encyclopaedic. Even non-climbers will enjoy his prose.