Thorne-Żytkow objects (TŻOs) are a theoretical class of star in which a compact neutron star is surrounded by a large, diffuse envelope. Supergiant TŻOs are predicted to be almost identical in appearance to red supergiants (RSGs), with their very red colors and cool temperatures placing them at the Hayashi limit on the H-R diagram. The only features that can be used at present to distinguish TŻOs from the general RSG population are the unusually strong heavy-element and lithium lines present in their spectra. These elements are the unique products of the stars fully convective envelope linking the photosphere with the extraordinarily hot burning region in the vicinity of the neutron star core. We have recently discovered a TŻO candidate in the Small Magellanic Cloud. It is the first star to display the distinctive chemical profile of anomalous element enhancements thought to be characteristic of TŻOs; however, up-to-date models and additional observable predictions (including potential asteroseismological signatures) are required to solidify this discovery. The definitive detection of a TŻO would provide the first direct evidence for a completely new model of stellar interiors, a theoretically predicted fate for massive binary systems, and never-before-seen nucleosynthesis processes that would offer a new channel for heavy-element and lithium production in our universe.