This letter introduces an efficient technique for pulse compression and dispersion compensation using microwave chirped pulses propagating through metamaterials in the negative refraction regime. To accomplish this, we investigated infinitely wide and 1-, 3-, 5-, and 7-cells-thick metamaterial slabs using a finite difference in the time-domain method and parameter extraction technique. We demonstrate that by controlling the chirp of the initial pulse, in association with the metamaterial cell density/geometry and frequency response, it is possible not only to compress the pulse (by a factor of 2), but also to compensate pulse broadening due to chromatic dispersion.