Pulses of light propagating through multiply scattering media undergo complex spatial and temporal distortions to form the familiar speckle pattern. There is much current interest in both the fundamental properties of speckles and the challenge of spatially and temporally refocusing behind scattering media. Here we report on the spatially and temporally resolved measurement of a speckle field produced by the propagation of an ultrafast optical pulse through a thick strongly scattering medium. By shaping the temporal profile of the pulse using a spectral phase filter, we demonstrate the spatially localized temporal recompression of the output speckle to the Fourier-limit duration, offering an optical analogue to time-reversal experiments in the acoustic regime. This approach shows that a multiply scattering medium can be put to profit for light manipulation at the femtosecond scale, and has a diverse range of potential applications that includes quantum control, biological imaging and photonics.