Three suggestions for your open:

• Use the three argument version
• Use lexical filehandles
• Use or not || for control flow.

open my $inputFH, '<', $pathToFile or die "Can't open $pathToFile for 
+reading.  Reason given = $!\n";
open my $outputFH, '>', $pathToFile2 or die "Can't open $pathToFile2 f
+or writing.  Reason given = $!\n";
while ($line = <$inputFH>)
{
    print $outputFH "Foo $line Baz\n";
}
[download]

Edit: Writing to a file opened for reading was silly.

I suspect you want something like this:

use strict;
open my $ALUS, "Z:\\3\' UTR intron project\\Alu_bed.bed"  or die "Coul
+dn't open alus: $!";

my %seen;
while (<$ALUS>){
    /(chr.*?)\t/ or next;
    if (! exists $seen{$1}){
      open my $fh, ">", "Z:\\3\' UTR intron project\\Alu_chroms\\$1.tx
+t"||die "couldn't open $1 file!";
      $seen{$1} = $fh;
    }
    print {$seen{$1}} "$_";
}
[download]

You might be better off to use a lexical hash to hold your filehandles rather than $1. You also ought to cater for the possibility of lines that don't match your pattern. I have changed your pattern, substituting a negated character class ([^\t]+) for your non-greedy .*? as that is perhaps safer.

In the code below I use a HEREDOC as my input and references to scalars (actually hash values) as my output just to avoid creating loads of files on my disk; the principle will work just as well with real files.

use strict;
use warnings;

open my $alusFH, q{<}, \ <<EOD or die qq{open: << HEREDOC: $!\n};
chrabc123    blah    blah
chrdef456    burble    blurgh
Duff line to be rejected
chrabc123    rootle    tootle
EOD

my %seen;
my %fileHandles;
my %outputFiles;

while ( <$alusFH> )
{
    if ( m{^(chr[^\t]+)\t} )
    {
        do {
           open $fileHandles{ $1 }, q{>}, \ $outputFiles{ $1 }
              or die qq{open: > scalar ref.: \n};
           } unless $seen{ $1 } ++;
        print { $fileHandles{ $1 } } $_;
    }
    else
    {
        warn qq{Bad line: $_};
    }
}

close $alusFH or die qq{close: << HEREDOC: $!\n};
do {
   close $fileHandles{ $_ }
      or die qq{close: > scalar ref.: \n};
   } for keys %fileHandles;

print qq{$_:\n\n$outputFiles{ $_ }----------\n}
   for sort keys %outputFiles;
[download]

Here's the output.

Bad line: Duff line to be rejected
chrabc123:

chrabc123    blah    blah
chrabc123    rootle    tootle
----------
chrdef456:

chrdef456    burble    blurgh
----------
[download]

I hope this is of interest.