The IceCube Neutrino Observatory has provided the first map of the high energy (~0.01 – 1 PeV) sky in neutrinos. Since neutrinos propagate undeflected, their arrival direction is an important identifier for sources of high energy particle acceleration. Reconstructed arrival directions are consistent with an extragalactic origin, with possibly a galactic component, of the neutrino flux. We present a statistical analysis of positional coincidences of the IceCube neutrinos with known astrophysical objects from several catalogs. For the brightest gamma-ray emitting blazars and for Seyfert galaxies, the numbers of coincidences is consistent with the random, or “null”, distribution. Instead, when considering starburst galaxies with the highest flux in gamma-rays and infrared radiation, up to n = 8 coincidences are found, representing an excess over the ~4 predicted for the null distribution. The probability that this excess is realized in the null case, the p-value, is p = 0.042. This value falls to p = 0.003 for a set of gamma-ray detected starburst galaxies and superbubbles in the galactic neighborhood. Therefore, it is possible that these might account for a subset of IceCube neutrinos. The physical plausibility of such correlation is discussed briefly.