The combination of inorganic semiconductors with organic thin films promises new strategies for the realization of complex hybrid optoelectronic devices. Oxidative chemical vapor deposition (oCVD) of conductive polymers offers a flexible and scalable path towards high-quality three-dimensional inorganic/organic optoelectronic structures. Here, hole-conductive poly(3,4-ethylenedioxythiophene) (PEDOT) grown by oxidative chemical vapor deposition is used to fabricate transparent and conformal wrap-around p-type contacts on three-dimensional microLEDs with large aspect ratios, a yet unsolved challenge in three-dimensional gallium nitride technology. The electrical characteristics of two-dimensional reference structures confirm the quasi-metallic state of the polymer, show high rectification ratios, and exhibit excellent thermal and temporal stability. We analyze the electroluminescence from a three-dimensional hybrid microrod/polymer LED array and demonstrate its improved optical properties compared with a purely inorganic microrod LED. The findings highlight a way towards the fabrication of hybrid three-dimensional optoelectronics on the sub-micron scale.