This is the wiki for chordal graphs. It states that "A perfect elimination ordering in a graph is an ordering of the vertices of the graph such that, for each vertex v, v and the neighbors of v that occur after v in the order form a clique. A graph is chordal if and only if it has a perfect elimination ordering.", but chordal graphs are only defined over the set of cyclic graphs with more than 3 vertices. Should this article be updated to "A graph is chordal if and only if it has a perfect elimination ordering and has more than 3 vertices"? Without the second constraint, we can consider $K_3$ to be chordal, but it is not chordal.
Let us look more closely at the definition of chordal graphs:
Definition. A graph $G = (V,E)$ is said to be chordal if every cycle of length $\geq 4$ has a chord. (Equivalently: it has no induced cycles of length four or more.)
Since $K_3$ does not have any cycle of length $\geq 4$, it is trivially chordal. Similarly, any tree is trivially chordal, for it does not have any cycles at all.