We demonstrate that, upon the chemisorption of organic molecules, Co thin films display a novel magnetic phase that we tentatively call Ferromagnetic Glass State. This is characterised by a giant magnetic hardening and by the violation of the Rayleigh law for magnetization reversal. Such new phase originates from the modification of the surface magnetic anisotropy induced by the molecule/film interaction, whose result is to produce a correlated random anisotropy field. The ferromagnetic glass state then emerges when the correlation length of the random anisotropy field is close to the characteristic exchange length that, in our case, is of the order of 10nm. At the microscopic level, the ferromagnetic glass state is defined by blurred pseudo-domains intertwined by diffuse and irregular domain walls. Intriguingly, the magnetization reversal process of such configuration terminates with vortex-like structures, predicted by theory and measured by magnetic-force microscopy. Our work shows how the strong electronic interaction of standard components, Co thin films and readily available molecules, can generate structures with remarkable new magnetic properties, and thus opens a new avenue for the design of tailored-on-demand magnetic composites.