Extensional flow properties of polymer solutions in volatile solvents govern many industrially-relevant coating processes, but existing instrumentation lacks the environment necessary to control evaporation. To mitigate evaporation during dripping-onto-substrate (DoS) extensional rheology measurements, we developed a chamber to enclose the sample in an environment saturated with solvent vapor. We validated the evaporation-controlled DoS device by measuring a model high molecular weight polyethylene oxide (PEO) in various organic solvents both inside and outside of the chamber. Evaporation substantially increased the extensional relaxation time lambda _{E} for PEO in volatile solvents like dichloromethane and chloroform. PEO/chloroform solutions displayed an over 20-fold increase in lambda _{E} due to the formation of an evaporation-induced surface film; evaporation studies confirmed surface features and skin formation reminiscent of buckling instabilities commonly observed in drying polymer solutions. Finally, the relaxation times of semi-dilute PEO/chloroform solutions were measured with environmental control, where lambda _{E} scaled with concentration by the exponent m=0.62. These measurements validate the evaporation-controlled DoS environment, and confirm that chloroform is a good solvent for PEO, with a Flory exponent of nu =0.54. Our results are the first to control evaporation during DoS extensional rheology, and provide guidelines establishing when environmental control is necessary to obtain accurate rheological parameters.