  Bions are multiple fractional instanton configurations with zero instanton
charge playing important roles in quantum field theories on a compactified
space with a twisted boundary condition. We classify fractional instantons and
bions in the $SU(N)$ principal chiral model on ${\mathbb R}^2 \times S^1$ with
twisted boundary conditions. We find that fractional instantons are global
vortices wrapping around $S^1$ with their $U(1)$ moduli twisted along $S^1$,
that carry $1/N$ instanton (baryon) numbers for the ${\mathbb Z}_N$ symmetric
twisted boundary condition and irrational instanton numbers for generic
boundary condition. We work out neutral and charged bions for the $SU(3)$ case
with the ${\mathbb Z}_3$ symmetric twisted boundary condition. We also find for
generic boundary conditions that only the simplest neutral bions have zero
instanton charges but instanton charges are not canceled out for charged bions.
A correspondence between fractional instantons and bions in the $SU(N)$
principal chiral model and those in Yang-Mills theory is given through a
non-Abelian Josephson junction.
