This paper presents the first garment capable of measuring brain activity with accuracy comparable to that of state-of-the art dry electroencephalogram (EEG) systems. The main innovation is an EEG sensor layer (i.e., the electrodes, the signal transmission, and the cap support) made entirely of threads, fabrics, and smart textiles, eliminating the need for metal or plastic materials. The garment is connected to a mobile EEG amplifier to complete the measurement system. As a first proof of concept, the new EEG system (Garment-EEG) was characterized with respect to a state-of-the-art Ag/AgCl dry-EEG system (Dry-EEG) over the forehead area of healthy participants in terms of: (1) skin-electrode impedance; (2) EEG activity; (3) artifacts; and (4) user ergonomics and comfort. The results show that the Garment-EEG system provides comparable recordings to Dry-EEG, but it is more susceptible to artifacts under adverse recording conditions due to poorer contact impedances. The textile-based sensor layer offers superior ergonomics and comfort compared to its metal-based counterpart. We provide the datasets recorded with Garment-EEG and Dry-EEG systems, making available the first open-access dataset of an EEG sensor layer built exclusively with textile materials. Achieving user acceptance is an obstacle in the field of neurotechnology. The introduction of EEG systems encapsulated in wearables has the potential to democratize neurotechnology and non-invasive brain-computer interfaces, as they are naturally accepted by people in their daily lives. Furthermore, supporting the EEG implementation in the textile industry may result in lower cost and less-polluting manufacturing processes compared to metal and plastic industries.