We present optical palpation, a tactile imaging technique for mapping micrometer- to millimeter-scale mechanical variations in soft tissue. In optical palpation, a stress sensor consisting of translucent, compliant silicone with known stress-strain behavior is placed on the tissue surface and a compressive load is applied. Optical coherence tomography (OCT) is used to measure the local strain in the sensor, from which the local stress at the sample surface is calculated and mapped onto an image. We present results in tissue-mimicking phantoms, demonstrating the detection of a feature embedded 4.7 mm below the sample surface, well beyond the depth range of OCT. We demonstrate the use of optical palpation to delineate the boundary of a region of tumor in freshly excised human breast tissue, validated against histopathology.