  Internal stellar magnetic fields are inaccessible to direct observations and
little is known about their amplitude, geometry and evolution. We demonstrate
that strong magnetic fields in the cores of red giant stars can be identified
with asteroseismology. The fields can manifest themselves via depressed dipole
stellar oscillation modes, which arises from a magnetic greenhouse effect that
scatters and traps oscillation mode energy within the core of the star. The
Kepler satellite has observed a few dozen red giants with depressed dipole
modes which we interpret as stars with strongly magnetized cores. We find field
strengths larger than $\sim\! 10^5 \,{\rm G}$ may produce the observed
depression, and in one case we infer a minimum core field strength of $\approx
\! \! 10^7 \,{\rm G}$.
