This paper presents the first garment capable of measuring EEG activity with accuracy comparable to state-of-the art dry EEG systems. The main innovation is an EEG sensor layer (i.e., the electrodes, the signal transmission, and the cap support) fully implemented as a garment, using threads, fabrics and smart textiles, without relying on any metal or plastic materials. The garment is interfaced via a connector to a mobile EEG amplifier to complete the measurement system. The new EEG system (Garment-EEG) has been 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) electrophysiological measurements (spontaneous and evoked 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 prone to getting affected by artifacts in adverse recording conditions due to poorer contact impedances. Ergonomics and comfort favor the textile-based sensor layer with respect to its metal-based counterpart. User acceptance is the main obstacle for EEG systems to democratize neurotechnology and non-invasive brain-computer interfaces. EEG sensor layers encapsulated in wearables have the potential to enable neurotechnology that is naturally accepted by people in their daily lives. Furthermore, by supporting the EEG implementation in the textile industry it is manufactured with lower cost and much less pollution compared to the metal and plastic industries.