  Amit, Linial, and Matou\vsek (Random lifts of graphs III: independence and
chromatic number, Random Struct. Algorithms, 2001) have raised the following
question: Is the chromatic number of random $h$-lifts of $K_5$ asymptotically
(for $h\to\infty$) almost surely equal to a single number? In this paper, we
offer the following partial result: The chromatic number of a random lift of
$K_5\setminus e$ is asymptotically almost surely three.
