The majority of patients in the neonatal intensive care unit (NICU) have pulmonary morbidities, yet little is known about the underlying parenchymal structure. We quantify parenchymal proton density and R2* in the lungs of quiet breathing, non-sedated neonates in the NICU using a multi-echo 3D radial UTE MRI. Results indicate that lung proton density decreases as expected with lung inflation, while R2* increases. A positive relationship between gravitational dependence and tissue density is also apparent, while R2* decreases in more gravitationally dependent regions. Overall, our findings support a negative relationship between tissue density and R2* in the neonatal lung.