We present the results of Very Large Array NH$_{3}$ $(J,K)=(1,1)$ and $(2,2)$ observations of the HH 111/HH 121 protostellar system. HH 111, with a spectacular collimated optical jet, is one of the most well-known Herbig-Haro objects. We report the detection of a new source (NH$_{3}-$S) in the vicinity of HH 111/HH 121 ($sim$0.03 pc from the HH 111 jet source) in two epochs of the ammonia observations. This constitutes the first detection of this source, in a region which has been thoroughly covered previously by both continuum and spectral line interferometric observations. We study the kinematic and physical properties of HH 111 and the newly discovered NH$_{3}-$S. We also use HCO$^{+}$ and HCN $(J=4-3)$ data obtained with the James Clerk Maxwell Telescope and archival Atacama Large Millimeter/submillimeter Array $^{13}$CO, $^{12}$CO, and C$^{18}$O $(J=2-1)$, N$_2$D$^{+}$ $(J=3-2)$, and $^{13}$CS $(J=5-4)$ data to gain insight into the nature of NH$_{3}-$S. The chemical structure of NH$_3-$S shows evidence for selective freeze-out, an inherent characteristic of dense cold cores. The inner part of NH$_3-$S shows subsonic non-thermal velocity dispersions indicating a coherent core, while they increase in the direction of the jets. Archival near- to far-infrared data show no indication of any embedded source in NH$_3-$S. The properties of NH$_3-$S and its location in the infrared dark cloud suggest that it is a starless core located in a turbulent medium with turbulence induced by Herbig-Haro jets and associated outflows. More data is needed to fully understand the physical and chemical properties of NH$_3-$S and if/how its evolution is affected by nearby jets.