The self-organization of an angular bis(uracil-ethynyl) benzene derivative is investigated on Ag(111) by means of scanning tunneling microscopy (STM) under ultrahigh vacuum (UHV) conditions. It is found - starting at low submonolayer coverage - that upon increasing the molecular coverage a disorder-to-order phase transformation occurs. Specifically, at low and intermediate molecular coverage a glassy phase consisting of one dimensional (1D) chains and 2D aggregates is observed, while close to a first complete molecular layer, a well-ordered 2D close-packed phase is revealed. The main driving forces responsible for the structure formation are: (i) the high self-complementarity of the uracil (U) moiety, resulting in U-U homopairs through twofold C=O•••H–N H-bonds; (ii) the steric hindrance induced in the system by the alkyl chains. The delicate balance between the molecule-molecule and the molecule-substrate interactions leads to a complex phase behavior of the uracil derivative at the solid-vacuum interface. On the basis of this detailed study, we present a qualitative understanding of the peculiar phase behavior of the system.