A little line shuffling and error checking fixes this:

use strict;
use warnings;

open (my $fh, "<", "testlines.txt") or die "$!";
local $/ = "\n\n";
while (<$fh>) {
    if ($_=~ /(third | four)/si) {
        chomp;
        print "line is: $_\n";
    }
}
close $fh;
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Code>perl test15.pl
line is: This is line one.
Line Two is this.
Third line starts here.
This is line four.
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