Keep the split simple and use splice to slice up the entries into appropriate size chunks:

#!/usr/bin/env perl
use strict;
use Data::Dumper;

my $line;
my @teams;
my @pending;

while ( $line = <DATA> ) {
    next if $line =~ /^#/ || $line =~ /^\s*$/;

    chomp $line;
    $line =~ s/^[^=]*\=//;
    push @pending, split /,/, $line;
    push @teams, [splice @pending, 0, 3] while @pending >= 3;
}

push @teams, \@pending if @pending;
print Dumper \@teams;

__DATA__
Teams=PATRIOTS,BILLS,DOLPHINS,JETS,COWBOYS,GIANTS,EAGLES,REDSKINS,BENG
+ALS,OILERS
Teams=STEELERS,BROWNS,SEAHAWKS,RAMS,49ERS,RAIDERS
[download]

Prints:

$VAR1 = [
          [
            'PATRIOTS',
            'BILLS',
            'DOLPHINS'
          ],
          [
            'JETS',
            'COWBOYS',
            'GIANTS'
          ],
          [
            'EAGLES',
            'REDSKINS',
            'BENGALS'
          ],
          [
            'OILERS',
            'STEELERS',
            'BROWNS'
          ],
          [
            'SEAHAWKS',
            'RAMS',
            '49ERS'
          ],
          [
            'RAIDERS'
          ]
        ];
[download]