$foo = join '', @{$chars};
$string =~ /^[\Q$foo\E]+$/;
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^ and $ to make sure it matches from beginning to end, and \Q and \E to make sure it puts a \ in front of non letters chars... If it returns true, you are all good
also... you could do

$string =~ /[^\Q$foo\E]/;
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and fail if that matches, would probably be faster since it stops as soon as it finds a character you don't want
                - Ant