Conformation statistics of macromolecules in dilute solution is one of the fundamental issues in polymer physics. Herein, we experimentally explore the average conformation of model randomly hyperbranched chains composed of uniform subchains near the theta point (T-theta,T-hyper). We have, for the first time, experimentally verified the size-mass scaling relation for model hyperbranched chains near T-theta,T-hyper. Quantitatively, the Flory exponent (nu) in the size-mass scaling < R > similar to (NtNb mu)-N-nu is determined to be nu approximate to 0.46 in good solvent toluene and to be 0.40 <= nu <= 0.47 in theta solvent cyclopentane. Our result agrees well with the theoretical prediction by Daoud and Joanny (nu = 7/16) near the theta point. Further, using molecular dynamics simulation, we demonstrate that probing the specific temperature region, at which model hyperbranched polymers exhibit a nu approximate to 0.5 size-mass scaling, would be a more appropriate way to find the real theta temperature for the highly branched systems in the simulation study. Overall, the present study clearly reveals that the size-mass scaling exponent of hyperbranched chains with uniform subchains is very close to 0.5 near the theta condition, which unambiguously illustrates the non-negligible role of three-body interaction in dominating the conformation of hyperbranched chains under the theta solvent condition.