We show that the PeV neutrinos detected by IceCube put unique constraints on "secret" interactions of neutrinos with the cosmic neutrino background (C\nuB). The coupling must be g <0.03 for the mediating boson mass m_{X} \lesssim 2 MeV, g/m_{X} < 5 GeV^{-1} for m_{X} \gtrsim 20 MeV, and $g/m_{X} <... Show more