The auditory-brainstem response (ABR) to short and simple acoustical signals is an important clinical tool used to diagnose the integrity of the brainstem. The ABR is also employed to investigate the auditory brainstem in a multitude of tasks related to hearing, such as processing speech or selectively focusing on one speaker in a noisy environment. Such research measures the response of the brainstem to short speech signals such as vowels or words. Because the voltage signal of the ABR has a tiny amplitude, several hundred to a thousand repetitions of the acoustic signal are needed to obtain a reliable response. The large number of repetitions poses a challenge to assessing cognitive functions due to neural adaptation. Here we show that continuous, non-repetitive speech, lasting several minutes, may be employed to measure the ABR. Because the speech is not repeated during the experiment, the precise temporal form of the ABR cannot be determined. We show, however, that important structural features of the ABR can nevertheless be inferred. In particular, the brainstem responds at the fundamental frequency of the speech signal, and this response is modulated by the envelope of the voiced parts of speech. We accordingly introduce a novel measure that assesses the ABR as modulated by the speech envelope, at the fundamental frequency of speech and at the characteristic latency of the response. This measure has a high signal-to-noise ratio and can hence be employed effectively to measure the ABR to continuous speech. We use this novel measure to show that the auditory brainstem response is weaker to intelligible speech than to unintelligible, time-reversed speech. The methods presented here can be employed for further research on speech processing in the auditory brainstem and can lead to the development of future clinical diagnosis of brainstem function.