Three dimensional (3D) magnetic field information on molecular clouds and cores is important for revealing their kinematical stability (magnetic support) against gravity which is fundamental for studying the initial conditions of star formation. In the present study, the 3D magnetic field structure of the dense starless core FeSt 1-457 is determined based on the near-infrared polarimetric observations of the dichroic polarization of background stars and simple 3D modeling. With an obtained angle of line-of-sight magnetic inclination axis $theta_{rm inc}$ of $45^{circ}pm10^{circ}$ and previously determined plane-of-sky magnetic field strength $B_{rm pol}$ of $23.8pm12.1$ $mu{rm G}$, the total magnetic field strength for FeSt 1-457 is derived to be $33.7pm18.0$ $mu{rm G}$. The critical mass of FeSt 1-457, evaluated using both magnetic and thermal/turbulent support is ${M}_{rm cr} = 3.70pm0.92$ ${rm M}_{odot}$, which is identical to the observed core mass, $M_{rm core}=3.55pm0.75$ ${rm M}_{odot}$. We thus conclude that the stability of FeSt 1-457 is in a condition close to the critical state. Without infalling gas motion and no associated young stars, the core is regarded to be in the earliest stage of star formation, i.e., the stage just before the onset of dynamical collapse following the attainment of a supercritical condition. These properties would make FeSt 1-457 one of the best starless cores for future studies of the initial conditions of star formation.
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