Emotional speech is one of the principal forms of social communication in humans. In this study, we investigated neural processing of emotional speech (happy, angry, sad and neutral) in the left hemisphere of 21 two-month-old infants using diffuse optical tomography. Reconstructed total hemoglobin (HbT) images were analysed using adaptive voxel-based clustering and region-of-interest (ROI) analysis. We found a distributed happy > neutral response within the temporo-parietal cortex, peaking in the anterior temporal cortex; a negative HbT response to emotional speech (the average of the emotional speech conditions < baseline) in the temporo-parietal cortex, neutral > angry in the anterior superior temporal sulcus (STS), happy > angry in the superior temporal gyrus and posterior superior temporal sulcus, angry < baseline in the insula, superior temporal sulcus and superior temporal gyrus and happy < baseline in the anterior insula. These results suggest that left STS is more sensitive to happy speech as compared to angry speech, indicating that it might play an important role in processing positive emotions in two-month-old infants. Furthermore, happy speech (relative to neutral) seems to elicit more activation in the temporo-parietal cortex, thereby suggesting enhanced sensitivity of temporo-parietal cortex to positive emotional stimuli at this stage of infant development.