Handheld imaging probes are needed to extend the clinical translation of optical elastography to in vivo applications, yet such probes have received little attention. In this paper, we present the first demonstration of optical palpation using a handheld probe. Optical palpation is a variant of optical elastography that uses three-dimensional optical coherence tomography (3D-OCT) to provide maps of stress at the tissue surface under static compression. Using this technique, stiff features present beneath the surface of turbid tissues are identified, providing mechanical contrast complementary to the optical contrast provided by OCT. However, during handheld operation, relative motion between the probe and the tissue can induce motion artifact, causing spatial distortion of 3D-OCT and in turn, optical palpation images. We overcome this issue using a novel, dual-function bi-layer that provides both a fiducial marker for co-registration and a compliant section for estimation of the stress at the tissue surface. Co-registration of digital photographs of the bi-layer laid out over the tissue surface is used to measure and correct for motion in the lateral (xy) plane. We also demonstrate, for the first time, that optical palpation can be used as a method for monitoring pressure applied to the tissue during handheld operation, thus providing a more repeatable and robust imaging technique between different users. Handheld optical palpation is demonstrated on a structured phantom, in vivo human skin and excised human breast tissue. In each case, image quality comparable to bench-top 3D-OCT and optical palpation is achieved.