use warnings;
use strict;


my $text= "start \\chapter{hello}\n end\n";

my $patternreadfromfile= "-- FOUND \$1 -- ";

my $inpattern = qr/\\chapter\{(.*)\}/;

# my $outpattern = q{$patternreadfromfile};
# # $outpattern eq '$patternreadfromfile'
# # outputs: 'start -- FOUND $1 --\n end'

my $outpattern = qq{ qq{$patternreadfromfile} };
# $outpattern eq 'qq{-- FOUND $1 -- }'
# eval($outpattern) eq '-- FOUND capture_group_1_contents -- '
# outputs: what you want (i think)

$text =~ s/$inpattern/$outpattern/gee;

print "$text\n";