Recent evidence for ethane clouds and condensation in Titan's atmosphere raise the question whether liquid ethane condensation nuclei and supercooled liquid ethane droplets exist under the prevalent conditions. We present laboratory studies on the phase behaviour of pure ethane aerosols and ethane aerosols formed in the presence of other ice nuclei under conditions relevant to Titan's atmosphere. Combining bath gas cooling with infrared spectroscopy, we find evidence for the existence of supercooled liquid ethane aerosol droplets. The observed homogeneous freezing rates imply that supercooled ethane could be a long-lived species in ethane-rich regions of Titan's atmosphere similar to supercooled water in the Earth's atmosphere.