Epilepsy is a chronic neurological disorder affecting more than 65 million people worldwide and manifested by recurrent unprovoked seizures. The unpredictability of seizures not only degrades the quality of life of the patients, but it can also be life-threatening. Modern systems monitoring electroencephalography (EEG) signals are being currently developed with the view to detect epileptic seizures in order to alert caregivers and reduce the impact of seizures on patients' quality of life. Such seizure detection systems employ state-of-the-art machine learning algorithms that require a large amount of labeled personal data for training. However, acquiring EEG signals during epileptic seizures is a costly and time-consuming process for medical experts and patients. Furthermore, this data often contains sensitive personal information, presenting privacy concerns. In this work, we generate synthetic seizure-like brain electrical activities, i.e., EEG signals, that can be used to train seizure detection algorithms, alleviating the need for sensitive recorded data. Our experiments show that the synthetic seizure data generated with our GAN model succeeds at preserving the privacy of the patients without producing any degradation in performance during seizure monitoring.