We compare APOGEE radial velocities (RVs) of young stars in the Orion A cloud with CO line gas emission and find a correlation between the two at large scales in agreement with previous studies. However, at smaller scales we find evidence for the presence of a substructure in the stellar velocity field. Using a friends-of-friends approach we identify 37 stellar groups with almost identical RVs. These groups are not randomly distributed, but form elongated chains or strings of stars with five or more members with low velocity dispersion across lengths of 1-1.5pc. The similarity between the kinematic properties of the APOGEE strings and the internal velocity field of the chains of dense cores and fibers recently identified in the dense interstellar medium is striking and suggests that for most of the Orion A cloud, young stars keep memory of the parental gas substructure where they originated.