In near-eye display systems that support three-dimensional (3D) augmented and virtual reality, a central factor in determining the user experience is the size of the eyebox. The eyebox refers to a volume where the eye receives an acceptable view of the image with respect to a set of criteria and thresholds. The size and location of this volume are primarily driven by optical architecture choices in which designers trade-off a number of constraints, such as field of view, image quality, and product design. It is thus important to clearly quantify how design decisions affect the properties of the eyebox. Recent work has started evaluating the eyebox in 3D based purely on optical criteria. However, such analyses do not incorporate perceptual criteria that determine visual quality, which are particularly important for binocular 3D systems. To address this limitation, we introduce the framework of a perceptual eyebox. The perceptual eyebox is the volume where the eye(s) must be located for the user to experience a visual percept falling within a perceptually-defined criterion. We combine optical and perceptual data to characterize an example perceptual eyebox for display visibility in augmented reality. The key contributions in this paper include: comparing the perceptual eyebox for monocular and binocular display designs, modeling the effects of user eye separation, and examining the effects of eye rotation on the eyebox volume.