During a recent online discussion, one of the participants made the claim that a Dyson sphere would be limited in mass by the Chandrasekhar limit. Attempts to solicit evidence for this claim were essentially unsuccessful. Though I am no expert on astrophysics, the claim in question seems dubious, because I am unaware that any putative Dyson sphere would be in a state of matter in which its collapse would be prevented solely by electron degeneracy pressure, as is the case in white dwarves. Moreover, I am unaware of any applications of the Chandrasekhar limit to any bodies other than white dwarves, so the claim makes no sense to me. Is there any way the material of a Dyson sphere could possibly attain the immense densities found in the insides of white dwarves?