Monolithic integration of III-V optoelectronic devices with materials for various functionalities inexpensively is always desirable. Polysilicon (poly-Si) is an ideal platform because it is dopable and semi-conducting and can be deposited and patterned easily on a wide range of low cost substrates. However, the lack of crystalline coherency in poly-Si poses an immense challenge for high-quality epitaxial growth. In this work, we demonstrate, for the first time, direct growth of micron-sized InGaAs/GaAs nanopillars on polysilicon. Transmission electron microscopy shows that the micron-sized pillars are single-crystalline and single Wurzite-phase, far exceeding the substrate crystal grain size ~100nm. The high quality growth is enabled by the unique tapering geometry at the base of the nanostructure, which reduces the effective InGaAs/Si contact area to < 40 nm in diameter. The small footprint not only reduces stress due to lattice mismatch but also prevents the nanopillar from nucleating on multiple Si crystal grains. This relaxes the grain size requirement for poly-Si, potentially reducing the cost for poly-Si deposition. Lasing is achieved in the as-grown pillars under optical pumping, attesting their excellent crystalline and optical quality. These promising results open up a pathway for low-cost synergy of optoelectronics with other technologies such as CMOS integrated circuits, sensing, nanofluidics, thin film transistor display, photovoltaics, etc.