While histological studies and conventional magnetic resonance imaging (MRI) investigations have elucidated the trajectory of structural changes in the developing brain, less is known regarding early functional cerebral development. Recent investigations have demonstrated that resting-state functional connectivity MRI (fcMRI) can identify networks of functional cerebral connections in infants. However, technical and logistical challenges frequently limit the ability to perform MRI scans early or repeatedly in neonates, particularly in those at greatest risk for adverse neurodevelopmental outcomes. High-density diffuse optical tomography (HD-DOT), a portable imaging modality, potentially enables early continuous and quantitative monitoring of brain function in infants. We introduce an HD-DOT imaging system that combines advancements in cap design, ergonomics, and data analysis methods to allow bedside mapping of functional brain development in infants. In a cohort of healthy, full-term neonates scanned within the first days of life, HD-DOT results demonstrate strong congruence with those obtained using co-registered, subject-matched fcMRI and reflect patterns of typical brain development. These findings represent a transformative advance in functional neuroimaging in infants, and introduce HD-DOT as a powerful and practical method for quantitative mapping of early functional brain development in normal and high-risk neonates.