Amyotrophic lateral sclerosis (ALS) is a rapidly progressive neurodegenerative disease of the motor system that leads to the impairment of speech and swallowing functions. The lack of a biomarker typically causes a diagnostic delay. To advance the current diagnostic process, we explored the feasibility of automatic detection of patients with ALS at an early stage from highly intelligible speech. A speech dataset was collected from thirteen newly diagnosed patients with ALS and thirteen age- and gender-matched healthy controls. Convolutional Neural Networks (CNNs), including time-domain CNN and frequency-domain CNN, were used to classify the intelligible speech produced by patients with ALS and those by healthy individuals. Experimental results indicated both time- and frequency-CNN outperformed standard neural network. The best sample-level sensitivity and specificity were obtained by time-CNN (71.6% and 80.9%, respectively). When multiple samples were used to vote to estimate a person-level performance, the best result was obtained by frequency-CNN (76.9% sensitivity and 92.3% specificity). Results demonstrated the possibility of early detection of ALS from intelligible speech signals.