Acquisition of high-resolution images from within internal organs using endoscopic optical imaging has numerous clinical applications. However, difficulties associated with optical aberrations and the trade-off between transverse resolution and depth-of-focus significantly limit the scope of applications. Here, we integrate a metalens, with the ability to modify the phase of incident light at sub-wavelength level, into the design of an endoscopic optical coherence tomography catheter (termed nano-optic endoscope) to achieve near diffraction-limited imaging through negating non-chromatic aberrations. Remarkably, the tailored chromatic dispersion of the metalens in the context of spectral interferometry is utilized to maintain high-resolution imaging beyond the input field Rayleigh range, easing the trade-off between transverse resolution and depth-of-focus. We demonstrate endoscopic imaging both in resected human lung specimens and in sheep airways in vivo. The combination of the superior resolution and higher imaging depth-of-focus of the nano-optic endoscope will likely increase the clinical utility of endoscopic optical imaging.