  Shearer gave a general theorem characterizing the family $\LLL$ of dependency
graphs labeled with probabilities $p_v$ which have the property that for any
family of events with a dependency graph from $\LLL$ (whose vertex-labels are
upper bounds on the probabilities of the events), there is a positive
probability that none of the events from the family occur.
  We show that, unlike the standard Lov\'asz Local Lemma---which is less
powerful than Shearer's condition on every nonempty graph---a recently proved
`Lefthanded' version of the Local Lemma is equivalent to Shearer's condition
for all chordal graphs. This also leads to a simple and efficient algorithm to
check whether a given labeled chordal graph is in $\LLL$.
