SignificanceUpon deformation, Newtonian fluids are expected to exhibit viscous behavior, and only when deformed on very short timescales, below the molecular diffusion time of a single molecule, is a solid-like elastic response expected. We have revealed a strong, rubber-like elasticity in the Newtonian fluid glycerol by analyzing the dynamics of a laser-driven free surface bubble. Not only do we find an elasticity persistent for four orders of magnitude longer than the diffusion time but also observe tolerance to large deformations only found in rubber-like materials. Our observations are independent of surface tension and require the existence of a transient state with solid-like long-range correlations different from the bulk state. This invites us to revisit our understanding of the liquid state.