We study dilepton production from a quark-gluon plasma of given energy density at finite quark chemical potential p and find that the dilepton production rate is a strongly decreasing function of p . Therefore, the signal to background ratio of dileptons from a plasma created in a heavy-ion collision rnay decrease significantly.PACS nurnbers. 25.75.+r. 12.38.Mh, 24.85.+p Quantum chromodynamics (QCD) ic nowadays believed to be the fundamental theory of strong interactions. Latttice Q C D calculations [ I ] exhibit a transition from normal nuclear matter to a phase of deconfined quarks and gluons, tlie so-called quark-gluon plasma (QGP). Presumably the early Universe was in this state up to about 10 psec nfter the big bang. Today one hopes to achieve sufficiently high energy densities to again create the Q G P in heavy-ion collision experiments.The plasma (if created) emits lots of particles. Among these, electromagnetic probes can leave the plasma volume without further interactions (due to their large mean free path) and are therefore especially suitable to carry information about its existence and properties (teinperature, energy, density, etc.). Thus, the production of real and virtual photons (the latter cnn be detected as dileptons, e.g., e + c -, p -1 is regurded as a possible signature for the Q G P [2-51. Many attcmpts arc niade to measure these particles in heavy-ion collision experiments [61.U p to now calculations of the dilepton production rate [2,3,51 neglected the baryo-chemical potential in the plasma. Then, the dilepton emission rate depends only on the plasma temperature. This temperature is related to the energy density E by the Stefan-Boltzmann law E-T~. if p ß =O. The energy density of the Q G P created in a collision can be readily estimated from the measured transverse energy and geometrical considerations [7,81 or HBT rneasureinents [91 of the plasma volume. This, in turn, allows the calculation of the total dilepton production rate from ewperiw~entall~~ n7easirrable qiranriries, without any assuniptions of a specific dynarnical model. Howcver, cxperiments [I01 and theory L111 indicatc that up to C E R N S P S energies : I sizable amount of baryon stopping occurs, i.e., the Bjorken skenario [I21 sccms not to be rcalistic for hcavy-ion collisions at these "moderate" energies. In Fact, even at R H I C bombarding energies & 5 200A GeV recent calculations using microscopic models [I 31 hint that the colliding heavy ions inay not be fully transparent. Consequently, it is possible that the baryon density (and thus p B ) in the Q G P does not vanish. In this case the dilepton production rate is, in (local) thermodynamical equilibriuin, a function of both temperature T und quark chemical potential p of the Q G P (we consider only U and d quarks, and therefore p = p ß / 3 ) . In tfie present Letter we study the influence of such nonvanishing quark chemical potential p on the dilepton production.Since the Stefan-Boltzmann relation E-T' does not hold for p / T > 0, we need to specify an equation...