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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. {\bf 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 \emph{Kepler} satellite has observed a few dozen red giants with suppressed dipole modes that we interpret as stars with strongly magnetized cores. We find field strengths larger than roughly $10^5 \,{\rm G}$ {\bf may produce} the observed suppression, and in one case {\bf we  infer a minimum core field strength of $\approx \! \! 10^7 \,{\rm G}$ }.