The functional neuroanatomy of speech processing has been investigated using positron emission tomography (PET) and functional magnetic resonance imaging (fMRI) for more than 20. years. However, these approaches have relatively poor temporal resolution and/or challenges of acoustic contamination due to the constraints of echoplanar fMRI. Furthermore, these methods are contraindicated because of safety concerns in longitudinal studies and research with children (PET) or in studies of patients with metal implants (fMRI). High-density diffuse optical tomography (HD-DOT) permits presenting speech in a quiet acoustic environment, has excellent temporal resolution relative to the hemodynamic response, and provides noninvasive and metal-compatible imaging. However, the performance of HD-DOT in imaging the brain regions involved in speech processing is not fully established. In the current study, we use an auditory sentence comprehension task to evaluate the ability of HD-DOT to map the cortical networks supporting speech processing. Using sentences with two levels of linguistic complexity, along with a control condition consisting of unintelligible noise-vocoded speech, we recovered a hierarchically organized speech network that matches the results of previous fMRI studies. Specifically, hearing intelligible speech resulted in increased activity in bilateral temporal cortex and left frontal cortex, with syntactically complex speech leading to additional activity in left posterior temporal cortex and left inferior frontal gyrus. These results demonstrate the feasibility of using HD-DOT to map spatially distributed brain networks supporting higher-order cognitive faculties such as spoken language.