This paper proposes a framework for studying competitive (pure) bundling in an oligopoly market. We find that under fairly general conditions, relative to separate sales, bundling raises market prices, benefits firms, and harms consumers when the number of firms is above a threshold (which can be small). This is in contrast to the findings in the duopoly case on which the existing literature often focuses. Our analysis also sheds new light on how consumer valuation dispersion affects price competition more generally.