We created a new high resolution (50-MHz) three-dimensional ultrasound biomicroscopy (3D-UBM) imaging system and applied it to the measurement of iridoconeal angle, an important biomarker for glaucoma patients. Glaucoma, a leading cause of blindness, often results from poor drainage of the fluid from the eye through structures located at the iridiocorneal angle. Measurement of the angle has important implications for predicting the course of the disease and determining treatment strategies. An angle measured at a particular location with conventional 2D-UBM can be biased due to tilt in the hand-held probe. We created a 3D-UBM system by automatically scanning a 2D UBM with a precision translating stage. Using 3D-UBM, we typically acqure several hundred 2D images to create a high-resolution volume of the anterior chamber of the eye. Image pre-processing included intensity based frame-to-frame alignment to reduce effects of eye motion, 3D noise reduction, and multi-planar reformatting to create rotational views along the optic-axis with the pupil at the center, thereby giving views suitable for measurement of the iridiocorneal angle. Anterior chambers were segmented using a semantic-segmentation convolutional neural network, which gave folded “leave-one-eye-out” accuracy of 98.04%±0.01%, sensitivity of 90.97%±0.02%, specificity of 98.91%±0.01%, and <i>Dice</i> coefficient of 0.91±0.04. Using segmentations, iridiocorneal angles were automatically estimated using a modification of the semi-automated trabecular- iris-angle method (TIA) for each of ∼360 rotational views. Automated measurements were compared to those made by four ophthalmologist readers in eight images from two eyes. In these images, an insignificant difference (p = 0.996) was shown between readers and automated results.