The statistical conformations of a length of polymer chain, such as DNA, trapped in a void within a gel under the influence of an external electric field, have been studied by the method of Green’s functions. Based upon a rectangular box approximation for the void shape, the method gives an explicit analytical expression for the end-to-end distance (R(x)) as a function of applied field strength, number of chain segments coiled within the void, and size of a chain segment. Results of calculations show that the field compresses the entrained coil into more compact configurations, as would be expected. Such compression is believed to affect the electrophoretic mobility of a long chain molecule like DNA in a dilute gel.