The 27 Al ( p , α ) 24 Mg reaction, which drives the destruction of 27 Al and the production of 24 Mg in stellar hydrogen burning, has been investigated via the Trojan Horse Method (THM), by measuring the 2 H ( 27 Al , α 24 Mg ) n three-body reaction. The experiment covered a broad energy range ( E c . m . ≤ 1.5 MeV ), aiming to investigate those of interest for astrophysics. The results confirm the THM as a valuable technique for the experimental study of fusion reactions at very low energies and suggest the presence of a rich pattern of resonances in the energy region close to the Gamow window of stellar hydrogen burning (70–120 keV), with potential impact on astrophysics. To estimate such an impact a second run of the experiment is needed, since the background due the three-body reaction hampered to collect enough data to resolve the resonant structures and extract the reaction rate.