  We study the hydrostatic equilibrium structure of compact stars in the
Eddington-inspired Born-Infeld gravity recently proposed by Banados and
Ferreira [Phys. Rev. Lett. 105, 011101 (2010)]. We also develop a framework to
study the radial perturbations and stability of compact stars in this theory.
We find that the standard results of stellar stability still hold in this
theory. The frequency square of the fundamental oscillation mode vanishes for
the maximum-mass stellar configuration. The dependence of the oscillation mode
frequencies on the coupling parameter \kappa of the theory is also
investigated. We find that the fundamental mode is insensitive to the value of
\kappa, while higher order modes depend more strongly on \kappa.
