Ever since the mid-1960’s, locking the phases of modes enabled the generation of laser pulses of duration limited only by the uncertainty principle, opening the field of ultrafast science. In contrast to conventional lasers, random lasers usually lack at least a mirror and generally emit broadband low-coherence light. They have, nevertheless, cavity modes that distinguish them from amplifiers and superluminescent light sources. Mode spacing in random lasers is ill-defined because optical feedback comes from scattering centres at random positions. Although progress has been made towards locking spatial and longitudinal modes in random lasers, the literature lacks reports on transform-limited pulse generation despite the many decades of the field. Here the generation of sub-nanosecond transform-limited pulses from a mode-locked random fibre laser is described. Exceedingly weak (<-73 dB) Rayleigh backscattering from decimetre-long sections of telecom fibre serves as laser feedback, providing narrow spectral selectivity to the Fourier limit. This unique laser is adjustable in pulse duration (0.34-20 ns), repetition rate (0.714-1.05 MHz) and can be temperature tuned. The high spectral-efficiency pulses are applied in distributed temperature sensing with 9.0 cm and 3.3x10-3 K resolution, exemplifying how the results can drive advances in the fields of spectroscopy, telecommunications, and sensing.