We propose a scheme for the emission of few-cycle dispersive waves in the midinfrared using hollow-core photonic crystal fibers filled with noble gas. The underlying mechanism is the formation of a plasma cloud by a self-compressed, subcycle pump pulse. The resulting free-electron population modifies the fiber dispersion, allowing phase-matched access to dispersive waves at otherwise inaccessible frequencies, well into the midinfrared. Remarkably, the pulses generated turn out to have durations of the order of two optical cycles. In addition, this ultrafast emission, which occurs even in the absence of a zero dispersion point between pump and midinfrared wavelengths, is tunable over a wide frequency range simply by adjusting the gas pressure. These theoretical results pave the way to a new generation of compact, fiber-based sources of few-cycle midinfrared radiation.