Thermodynamic noise places a fundamental limit on the frequency stability of dielectric optical resonators. Here, we present the characterization of thermorefractive noise in photonic-chip-based silicon-nitride (Si3N4) microresonators and show that thermorefractive noise is the dominant thermal noise source in the platform. We employed balanced homodyne detection to measure the thermorefractive noise spectrum of microresonators of different diameters. The measurements are in good agreement with theoretical models and finite element method simulations. Our characterization sets quantitative bounds on the scaling and absolute magnitude of thermal noise in photonic-chip-based microresonators. An improved understanding of thermorefractive noise can prove valuable in the design considerations and performance limitations of future photonic integrated devices.