A variation that doesn't use unpack:

@triplets0 = $line            =~ /(...)/g;
@triplets1 = substr($line, 1) =~ /(...)/g;
@triplets2 = substr($line, 2) =~ /(...)/g;
[download]

or even

push(@triplets, [ substr($line, $_) =~ /(...)/g ]) for 0..2;
[download]

Finally, a solution for arbitrary group sizes:

$group_size = 3;
push(@groups, [ substr($line, $_-1) =~ /(.{$group_size})/g ])
   for 1..$group_size;
[download]

If you don't care to group them, remove the square brackets.

Test:

$line = 'atccatccctttaat';

push(@triplets, [ substr($line, $_) =~ /(.{$_})/g ]) for 0..2;

require Data::Dumper;
print(Data::Dumper::Dumper(\@triplets));

__END__
output
======
$VAR1 = [
          [
            'atc',
            'cat',
            'ccc',
            'ttt',
            'aat'
          ],
          [
            'tcc',
            'atc',
            'cct',
            'tta'
          ],
          [
            'cca',
            'tcc',
            'ctt',
            'taa'
          ]
        ];
[download]