TaSe3 belongs to a class of low-dimensional materials characterized by the interplay and competition between dimensionality crossover and broken symmetry ground states. A comprehensive study by dc-transport, optical, and angle-resolved photoemission (ARPES) experiments shows that the electronic properties of this compound are strongly anisotropic between the chain and the transverse crystallographic direction. Even though TaSe3 fails to undergo a charge-density-wave (CDW) phase transition, we found evidence for short range order CDW segments, which progressively disappear with decreasing temperature.