  Thorne-\.Zytkow objects (T\.ZOs) are a class of stellar object comprised of a
neutron star core surrounded by a large and diffuse envelope. Their exterior
appearance is identical to red supergiants; the distinctive electromagnetic
signature of a T\.ZO is a suite of unusual chemical abundance patterns,
including excesses of Li, Rb, Mo, and Ca. However, electromagnetic observations
cannot unambiguously identify the presence of a neutron star core. Detection of
continuous gravitational wave emission from a rotating neutron star core would
provide strong supporting evidence for the existence of T\.ZOs. We present a
model for gravitational wave detector confirmation of T\.ZOs and demonstrate
that these objects should be detectable with Advanced LIGO. We also investigate
possible targets for joint optical and gravitational searches, and comment on
prospects for detectability in both current and future gravitational wave
detector networks.
