The initial stages of biofilm formation at a surface are triggered by the surface association of individual microorganisms. The biological mechanisms and interfacial interactions underlying microbial adhesion to surfaces have been widely studied for bacteria, while microalgae remained rather unconsidered despite their technological relevance, e.g., in photo-bioreactors. We performed in vivo micropipette force measurements with the model organism Chlamydomonas reinhardtii, a unicellular eukaryotic microalga that dwells in liquid-infused soils and on moist rocks. We characterize the adhesion forces and dissect the influence of intermolecular interactions by probing the adhesion forces of single cells on different model substrates with tailored properties. Our experiments show that the flagella-mediated adhesion of Chlamydomonas to surfaces is largely substrate independent, enabling the cell to adhere to any type of surface. This universal adhesion mechanism allows the microalga to effectively colonize abiotic surfaces in their heterogeneous natural habitats. Our results reveal a dominant contribution of electrostatic interactions governing microalgal adhesion and suggest that flagella membrane processes may cause significant variations of the adhesive properties of the flagella.