We present data on dielectron emission in proton induced reactions on a Nb target at 3.5 GeV kinetic beam energy measured with HADES installed at GSI. The data represent the first high statistics measurement of proton-induced dielectron radiation from cold nuclear matter in a kinematic regime, where strong medium effects are expected. Combined with the good mass resolution of 2%, it is the first measurement sensitive to changes of the spectral functions of vector mesons, as predicted by models for hadrons at rest or small relative momenta. Comparing the e+e− invariant mass spectra to elementary p + p data, we observe for e+e− momenta Pee<0.8 GeV/c a strong modification of the shape of the spectrum, which we attribute to an additional ρ-like contribution and a decrease of ω yield. These opposite trends are tentatively interpreted as a strong coupling of the ρ meson to baryonic resonances and an absorption of the ω meson, which are two aspects of in-medium modification of vector mesons. The QCD vacuum is characterized by nonzero expectation values of various quark and gluon operators. Most notable is the finite chiral quark condensate, signaling the spontaneous breaking of chiral symmetry. In a cold strongly interacting medium, the chiral condensate is expected to be modified (in linear density approximation, by about 30% at nuclear saturation density). As predicted by various models [1], [2], [3], [4], [5], [6], [7], [8] and [9], vector meson properties should be affected by changes of the condensates. Such phenomena can be studied in leptonic decays of the vector mesons (e.g. V→e+e−, with V=ρ,ω,ϕ). According to [10] the ρ meson is especially sensitive to changes of those condensates which break chiral symmetry (also called chirally odd condensates). In hadronic many-body approaches many hints have been found for a broadening of the ρ meson spectral function in an ambient nuclear medium [5], [6], [11] and [12]. Experimentally, in-medium properties can be studied in heavy-ion collisions (probing hot and dense hadronic matter) or in proton-, pion- or photon-induced reactions on nuclei (probing cold nuclear matter). For recent reviews on medium effects in cold nuclear matter see in particular [6] and [7]. Medium modifications are expected to be stronger in heavy-ion collisions due to the higher densities and temperatures. Measured observables represent an average over the complete space-time evolution of the temperature and the density of the system. On the other hand, in proton-, pion- or photon-induced reactions the system does not undergo a noticeable density and temperature evolution in time hence conditions of the system are better defined. Electron pair (e+e−) decay of vector mesons is an ideal probe for such studies since electrons and positrons are not affected by strong final state interactions. A promising observable is the spectral shape, i.e. the e+e− invariant mass distribution, but also the nuclear modification of the cross section provides valuable information since it is connected to the total widths of the hadrons inside the medium. The latter reflect also the coupling of mesons to resonance hole states, which is an important element of the in-medium self energy of propagating mesons. However, two competing mechanisms have to be considered when discussing the nuclear modifications. Multi-step production mechanisms can enhance the particle production, while absorption of the produced hadrons reduces the detectable yields. Both contributions have to be considered before drawing solid conclusions about the hadron widths inside the medium. A measurement sensitive to the spectral shape on the other hand requires that the decay takes place inside the nucleus. Therefore good acceptance for decays of low momentum vector mesons is of crucial importance, in particular for the relatively long living ω and ϕ mesons. In fact all measurements focusing on the spectral distribution of dielectrons produced off nuclei in photon and proton induced reactions are restricted to relatively high momenta (Pee>0.8 GeV/c) and are not conclusive yet. For the ρ meson, the CLAS experiment at JLab [13] reports a slight broadening and no shift of the ρ pole mass in photon induced reactions, while the E325 experiment at KEK [14] deduced a shift but no broadening in proton induced reactions. For the ω and ϕ mesons, experiments [15], [16], [17] and [18] report a sizable collisional broadening (up to a factor 16 larger than the natural line width in case of the ω) inside the medium extracted by comparing the nuclear modification of the cross sections to microscopic transport models. Besides the complications due to additional yield fed by pion driven secondary collisions inside the nucleus, the disadvantage of these indirect measurements is their model dependence. For instance, the recent analysis of [19] led to a significantly different width of the ω meson inside the medium as extracted in [15]. In this Letter we report on inclusive e+e− pair production in proton induced reactions at Ekin=3.5 GeV on the nucleus Nb, representing the first high statistics measurement with small momenta of e+e− pairs relative to the medium (Pee<0.8 GeV/c), see Fig. 1. By comparing the p + Nb data to e+e− production from elementary p + p collisions at the same kinetic beam energy [20], the presented results are sensitive to both above discussed observables, namely line shape modifications and nuclear suppression of the production cross section.