The polarization discontinuity across interfaces in polar nitride-based heterostructures can lead to the formation of two-dimensional electron and hole gases. In the past, the observation of these electron and hole gases has been achieved through various experimental techniques, most often by electronic measurements but occasionally by optical means. However, the occurrence of a two-dimensional hole gas has never been demonstrated optically in nitride-based heterostructures. The objective of this article is to demonstrate, thanks to the combination of various optical spectroscopy techniques coupled to numerical simulations, the presence of a two-dimensional hole gas in a GaN/AlGaN/GaN heterostructure. This is made possible thanks to a GaN/AlGaN/GaN heterostructure displaying a micrometer-thick AlGaN layer and a GaN cap thicker than in conventional GaN-based HEMTs structures. The band structure across the whole heterostructure was established by solving self-consistently the Schrödinger and Poisson equations and by taking into account the experimentally determined strain state of each layer. The appearance of a two-dimensional hole gas in such structure is thus established first theoretically. Continuous and quasicontinuous photoluminescence, spanning six orders of magnitude excitation intensities, reveal the presence of a broad emission band at an energy around 50 meV below the exciton emission and whose energy blueshifts with increasing excitation power density, until it is completely quenched due to the complete screening of the internal electric field. Time-resolved measurements show that the emission arising from the two-dimensional hole gas can be assigned to the recombination of holes in the potential well with electrons located in the top GaN as well as electron from the bottom AlGaN, each of them displaying different decay times due to unequal electric fields. Besides the optical demonstration of a two-dimensional hole gas in a nitride-based heterostructure, our work highlights the rich optical recombination processes involved in the emission from such a hole gas.