The hydride NdCoSiH obtained by exposure at 523 K of the ternary antiferromagnet NdCoSi under a pressure of 4 MPa of hydrogen crystallizes in the tetragonal ZrCuSiAs-type structure where H atoms occupy the tetrahedral [Nd-4] site. The hydrogenation induces an increase in the unit cell volume close to 6%. The investigation of NdCoSiH by magnetization measurements reveals its ferromagnetic behavior below T-C = 20.5(5) K. Neutron powder diffraction shows that the T-C temperature is associated with a ferromagnetic arrangement of the Nd moments (2.3(2)mu(B) at 1.5 K) parallel to the c axis as observed for NdFeSi. The magnetic properties, magnetic structure, and the value of the Nd ordered magnetic moment evidenced for NdCoSiH are discussed using both band structure calculations and a comparison with the behavior of NdCoSi and NdFeSi.