A presence of a penumbra is one of the main properties of a mature sunspot, and its formation mechanism has been elusive due to a lack of observations that fully cover the formation process. Utilizing the New Solar Telescope at the Big Bear Solar Observatory, we observed the formation of a partial penumbra for about 7 hours simultaneously at the photospheric (TiO; $7057{AA}$) and the chromospheric ($H{alpha}$, $-1{AA}$) spectral lines with high spatial and temporal resolution. From this uninterrupted, long observational sequence, we found that flux emergence under the stable chromospheric canopy fields resulted in penumbra formation, while emerging flux under the expanding chromospheric fields appeared as transient elongated granules. Based on these findings, we suggest a possible scenario for penumbra formation in which a penumbra forms when the emerging flux is constrained from continuing to emerge, but rather is trapped at the photospheric level by the overlying chromospheric canopy fields.