Single-molecule fluorescence studies of functional biomolecule dynamics rely on the ability to provide biologically relevant experimental conditions. Long measurement times on single molecules require their immobilization, which might modify their dynamics through interactions with the trapping medium, e.g., a class surface or a polymer gel. In an effort to to overcome this problem we have devised a new immobilization technique, based on the confinement of single biomolecules inside 100 nm surface-tethered lipid vesicles. The number of molecules in each vesicle can be accurately determined from fluorescence time traces; under our experimental conditions the number distribution of encapsulated molecules obeys a Poisson distribution with an average occupancy of 0.65 molecules per vesicle. It is further shown that the distribution of fluorescence polarization values of trapped molecules can serve as a sensitive probe for their freedom of motion and thus for the environment they sample inside the liposomes. Polarization distributions are obtained for two vesicle-entrapped labeled proteins, bovine serum albumin and adenylate kinase, and compared with distributions measured for the same proteins directly adsorbed on glass. From the significant relative narrowing of the distributions for encapsulated molecules, it is concluded that their motion within the vesicles is quite similar to free solution.