We present a new wearable electrooculogram (EOG) monitor for measuring eye movements. We fabricated conductive and flexible graphene-based textiles from nylon to use as a sensing electrode, which we then integrated into a commercially available eye mask held in place only with the standard elastic strap. We tested this mask on 4 participants to quantify the noise floor and show that we can detect eye blinks to a high SNR of over 16 dB. We also identify that the material can detect other eye movements in cases when the noise floor is low. As our system is held in place with only an elastic strap it offers the same level of comfort as when wearing a normal eye mask. Our sensors offer an increased level of comfort over conventional gelled electrodes traditionally used in EOG monitoring and may be of use for comfortable eye movement experiments. This is particularly important during sleep studies where the EOG is routinely monitored, but using bulky instrumentation.