High-resolution angle-resolved photoemission (ARPES) displays quasi-one dimensional (1D) electronic states in the insulating molybdenum red bronze K0.33MoO3, in good qualitative agreement with band structure calculations. Combined ARPES, optical conductivity, and electrical resistivity data underline the importance of defects which pin the Fermi level within the gap. The ARPES line shape exhibits the same strong-coupling features observed in the blue bronze K0.3MoO3, a related 1D Peierls conductor. We speculate that a similar mechanism could be at the origin of the gaps in both materials.