  A chordal graph is a graph with no induced cycles of length at least $4$. Let
$f(n,m)$ be the maximal integer such that every graph with $n$ vertices and $m$
edges has a chordal subgraph with at least $f(n,m)$ edges. In 1985 Erd\H{o}s
and Laskar posed the problem of estimating $f(n,m)$. In the late '80s,
Erd\H{o}s, Gy\'arf\'as, Ordman and Zalcstein determined the value of
$f(n,n^2/4+1)$ and made a conjecture on the value of $f(n,n^2/3+1)$. In this
paper we prove this conjecture and answer the question of Erd\H{o}s and Laskar,
determining $f(n,m)$ asymptotically for all $m$ and exactly for $m \leq
n^2/3+1$.
