We present what is to our knowledge the first longitudinal coherence measurement of a transient inversion collisional x-ray laser. We investigated the picosecond output of a Ni-like Pd x-ray laser at 14.68 nm generated by the COMET laser facility at the Lawrence Livermore National Laboratory. Interference fringes were generated with a Michelson interferometer setup in which a thin multilayer membrane was used as a beam splitter. We determined the longitudinal coherence for the 4d1S0 --> 4p1P1 lasing transition to be approximately 400 microm (1/e half-width) by changing the length of one interferometer arm and measuring the resultant variation in fringe visibility. The inferred gain-narrowed linewidth of approximately 0.29 pm is a factor of 4 less than previously measured in quasi-steady-state x-ray laser schemes.