  We construct minimal electronic models for a newly discovered superconductor
LaO$_{1-x}$F$_x$BiS$_2$ ($T_c=$ 10.6K) possessing BiS$_2$ layers based on first
principles band calculation. First, we obtain a model consisting of two Bi $6p$
and two S $3p$ orbitals, which give nearly electron-hole symmetric bands.
Further focusing on the bands that intersect the Fermi level, we obtain a model
with two $p$ orbitals. The two bands (per BiS$_2$ layer) have
quasi-one-dimensional character with a double minimum dispersion, which gives
good nesting of the Fermi surface. At around $x\sim 0.5$ the topology of the
Fermi surface changes, so that the density of states at the Fermi level becomes
large. Possible pairing states are discussed.

Superconductivity