BY PLANE: The nearest airport is Geneva. From here Ouibus run a service directly to Chamonix (you will need to pre-book)
BY TRAIN: It is possible to reach Chamonix by rail, via nearby St-Gervais-les-Bains. Trains run to St-Gervais-les-Bains from Paris, Lyon and Nice (among other destinations).
BY BUS: Ouibus run services directly to Chamonix from Paris, Lyon and Geneva.