  Borromean rings and Borromean binding, a class of intriguing phenomena as
three objects are linked (bound) together while any two of them are unlinked
(unbound), widely exist in nature and have been found in systems of biology,
chemistry and physics. Previous studies have suggested that the occurrence of
such a binding in physical systems typically relies on the microscopic details
of pairwise interaction potentials at short-range, and is therefore
non-universal. Here, we report a new type of Borromean binding in ultracold
Fermi gases with Rashba spin-orbit coupling, which is {\it universal} against
short-range interaction details, with its binding energy only dependent on the
s-wave scattering length and the spin-orbit coupling strength. We show that the
occurrence of this universal Borromean binding is facilitated by the symmetry
of the single-particle dispersion under spin-orbit coupling, and is therefore
{\it symmetry-selective} rather than interaction-selective. The state is robust
over a wide range of mass ratio between composing fermions, which are
accessible by Li-Li, K-K and K-Li mixtures in cold atoms experiments. Our
results reveal the importance of symmetry factor in few-body physics, and shed
light on the emergence of new quantum phases in a many-body system with exotic
few-body correlations.
