The dynamics of a molecule immersed in a superfluid medium are considered. Results are derived using a classical hydrodynamic approach followed by canonical quantization. The classical model, a rigid body immersed in incompressible fluid, permits a thorough analysis; its effective Hamiltonian generalizes the usual rigid-rotor Hamiltonian. In contrast to the free rigid rotor, the immersed body is shown to have chaotic dynamics. Quantization of the classical model leads to new and experimentally verifiable features. It is shown, for instance, that chiral molecules can behave as "quantum propellers:" the rotational-translational coupling induced by the superfluid leads to a nonzero linear momentum in the ground state. Hydrogen peroxide is a strong candidate for experimental detection of this effect. The signature is a characteristic splitting of rotational absorption lines. The 1(01)-->1(10) line in hydrogen peroxide, for example, is predicted to split into three lines separated by as much as 0.01 cm(-1), which is about the experimental linewidth.