The Cosmic Microwave Background (CMB) yields information about our Universe at around 380,000 years after the Big Bang (BB). Due to the weak interaction of the neutrinos with matter, the Cosmic Neutrino Background (CNB) should give information about a much earlier time of our Universe, around one second after the BB. Probably, the most promising method to “see” the CNB is the capture of the electron neutrinos from the Background by Tritium, which then decays into ³He and an electron with the energy of the the [Formula: see text]-value [Formula: see text] 18.562[Formula: see text]keV plus the electron neutrino rest mass. The “KArlsruhe TRItium Neutrino” (KATRIN) experiment, which is in preparation, seems presently the most sensitive proposed method for measuring the electron antineutrino mass. At the same time, KATRIN can also look by the reaction [Formula: see text]. The capture of the Cosmic Background Neutrinos (CNB) should show in the electron spectrum as a peak by the electron neutrino rest mass above [Formula: see text]. Here, the possibility to see the CNB with KATRIN is studied. A detection of the CNB by KATRIN seems not to be possible at the moment. But KATRIN should be able to determine an upper limit for the local electron neutrino density of the CNB.