An ultrafast electron diffraction facility with an overall temporal resolution of 31 fs root mean square is developed. Even for a charge as high as 0.6 pC, the electron bunch duration and timing jitter are 25 fs and less than 10 fs, respectively. Stroboscopic visualization of nuclear or electron dynamics in atoms, molecules or solids requires ultrafast pump and probe pulses and a close to perfect synchronization between the two. We have developed a 3 MeV ultrafast electron diffraction (UED) probe technology that nominally reduces the electron bunch duration and the arrival time jitter to the subfemtosecond level. This simple configuration uses a radiofrequency photogun and a 90 degrees achromatic bend and is designed to provide effectively jitter-free conditions. Terahertz streaking measurements reveal an electron bunch duration of 25 fs, even for a charge as high as 0.6 pC, and an arrival time jitter of 7.8 fs, the latter limited by only the measurement accuracy. From pump-probe measurements of photoexcited bismuth films, the instrument response function was determined to be 31 fs. This pioneering jitter-free technique paves the way towards UED of attosecond phenomena in atomic, molecular and solid-state dynamics.