We investigate linear electronic transport in single-walled carbon nanotubes with two intramolecular tunneling barriers. The one-dimensional character of transport in these molecular wires is reflected in unconventional Coulomb blockade features, occurring for thermal lengths larger than the width of the one-dimensional dot. In this regime, long ranged Luttinger liquid correlations among tunneling events on and off the island invalidate a conventional incoherent sequential tunneling picture. In contrast, correlated sequential tunneling and co-tunneling dominate transport at resonance. This results, for instance, in the power-law temperature dependence Gmax∝Tαend−end−1 of the conductance maximum, typical for tunneling between the ends of two Luttinger liquids. Our predictions are in agreement with recent measurements in carbon nanotube intramolecular quantum dots.