Increases in speed and sensitivity enabled rapid clinical adoption of optical coherence tomography (OCT) in ophthalmology. Recently, visible-light OCT (vis-OCT) achieved ultrahigh axial resolution, improved tissue contrast, and provided new functional imaging capabilities, demonstrating the potential to improve clinical care further. However, limited speed and sensitivity caused by the high relative intensity noise (RIN) in supercontinuum lasers impeded the clinical adoption of vis-OCT. To overcome these limitations, we developed balanced-detection vis-OCT (BD-vis-OCT), which uses two calibrated spectrometers to cancel RIN and other noises. We analyzed the RIN to achieve robust subpixel calibration between the two spectrometers and showed that BD-vis-OCT reduced the A-line noise floor by up to 20.5 dB. Metrics comparing signal-to-noise-ratios showed similar image qualities across multiple reference arm powers, a hallmark of operation near the shot-noise limit. We imaged healthy human retinas at an A-line rate of 125 kHz and a field-of-view up to 10 mm ×4 mm. We found that BD-vis-OCT revealed retinal anatomical features previously obscured by the noise floor.