Ammonia is one of the best tracers of cold dense cores. It is also a minor constituent of interstellar ices and, as such, one of the important nitrogen reservoirs in the protosolar nebula, together with the gas phase nitrogen, in the form of N2 and N. An important diagnostic of the various nitrogen sources and reservoirs of nitrogen in the Solar System is the 14N/15N isotopic ratio. While good data exist for the Solar System, corresponding measurements in the interstellar medium are scarce and of low quality. Following the successful detection of the singly, doubly, and triply deuterated isotopologues of ammonia, we have searched for 15NH2D in dense cores, as a new tool for investigating the 14N/15N ratio in dense molecular gas. With the IRAM-30m telescope, we have obtained deep integrations of the ortho 15NH2D (1(1,1)-1(0,1)) line at 86.4 GHz, simultaneously with the corresponding ortho NH2D line at 85.9 GHz. o-15NH2D is detected in Barnard-1b, NGC1333-DCO+, and L1689N, while we obtained upper limits towards LDN1544 and NGC1333-IRAS4A, and a tentative detection towards L134N(S). The 14N/15N abundance ratio in NH2D ranges between 350 and 850, similar to the protosolar value of ~ 424, and likely higher than the terrestrial ratio of 270.