Machine learning (ML) is revolutionizing research and industry. Many ML applications rely on the use of large amounts of personal data for training and inference. Among the most intimate exploited data sources is electroencephalogram (EEG) data, a kind of data that is so rich with information that application developers can easily gain knowledge beyond the professed scope from unprotected EEG signals, including passwords, ATM PINs, and other intimate data. The challenge we address is how to engage in meaningful ML with EEG data while protecting the privacy of users. Hence, we propose cryptographic protocols based on Secure Multiparty Computation (SMC) to perform linear regression over EEG signals from many users in a fully privacy-preserving (PP) fashion, i.e.~such that each individual's EEG signals are not revealed to anyone else. To illustrate the potential of our secure framework, we show how it allows estimating the drowsiness of drivers from their EEG signals as would be possible in the unencrypted case, and at a very reasonable computational cost. Our solution is the first application of commodity-based SMC to EEG data, as well as the largest documented experiment of secret sharing based SMC in general, namely with 15 players involved in all the computations.