In this paper, we investigate the fundamental limits of reliable communication over a discrete memoryless channel (DMC) when there are a large number of noisy views of a transmitted symbol, i.e., when several copies of a single symbol are sent independently through the DMC. We argue that the channel capacity and dispersion of such a \emph{multi-view} DMC converge exponentially quickly in the number of views to to the entropy and varentropy of the input distribution, respectively, and identify the exact rate of convergence. This rate equals the smallest Chernoff information between two conditional distributions of the output given unequal inputs. We also present a new channel model that we call the \emph{Poisson approximation channel}---of possible independent interest---whose capacity closely approximates the capacity of the multi-view binary symmetric channel (BSC).