Obstructive sleep apnea (OSA) is a sleep disorder in which pharyngeal collapse during sleep, causes a complete or partial airway obstruction. OSA is common and can have severe impacts, but often remains unrecognized. In this study, we propose a novel method which able to detect OSA subjects while they are awake, by analyzing breathing sounds during speech. The hypothesis is that OSA is associated with anatomical and functional abnormalities of the upper airway, which in turn, affect the acoustic parameters of a natural breathing sound during speech. The proposed OSA detector is a fully automated system, which consists of three consecutive steps including: 1) locating breathing sounds during continuous speech, 2) extracting acoustic features that quantify the breathing properties, and 3) OSA/non-OSA classification based on the detected breathing sounds. Based on breathing sounds analysis alone (90 male subjects; 72 for training, 18 for validation), our system yields an encouraging results (accuracy of 76.5%) showing the potential of speech analysis to detect OSA. Such a system can be integrated with other non-contact OSA detectors to provide a reliable and OSA syndrome-screening tool.