  The dichromatic number of a directed graph is at most 2, if we can 2-color
the vertices such that each monochromatic part is acyclic. An oriented graph
arises from a graph by orienting its edges in one of the two possible
directions. We study oriented graphs, which have dichromatic number more than
2. Such a graph $D$ is $3$-dicritical if the removal of any arc of $D$ reduces
the dichromatic number to 2. We construct infinitely many $3$-dicritical
oriented graphs. Neumann-Lara found the four $7$-vertex $3$-dichromatic
tournaments. We determine the $8$-vertex $3$-dichromatic tournaments, which do
not contain any of these, there are $64$ of them. We also find all
$3$-dicritical oriented graphs on $8$ vertices, there are $159$ of them. We
determine the smallest number of arcs that a $3$-dicritical oriented graph can
have. There is a unique oriented graph with $7$ vertices and $20$ arcs.
