  Inspired by the discovery of high temperature superconductivity in
potassium-doped $p$-terphenyl, we examine the possibility of superconductivity
in $p$-quaterphenyl with one more phenyl ring than $p$-terphenyl. The Meissner
effect with critical temperatures ranging from 3.5 K to 120 K is found by the
magnetic susceptibility measurements in $p$-quaterphenyl upon doping potassium
in the condition of annealing or just pestling. The primary superconducting
phase with critical temperature of 7.2 K can be reduplicated in several
superconducting samples. In both the annealed and pestled superconducting
samples, the observation of bipolaronic character by the Raman scattering
measurements reveals the close relationship between bipolarons and
superconductivity. The occurrence of superconductivity in potassium-doped
$p$-quaterphenyl provides an indication that chain link organic molecules are
potential candidates for high temperature superconductors.
