There is a Readonly module. This is not the same const, as a Readonly::Hash is slower than a normal Hash.

You might consider making your data an object. Then it's use will be clearer, and you can control access if you need to.

package ChessMoves;

sub new
{
    my $class = shift;

    return bless {0 => { 0 => [
                 [[1, 0],[2, 0],[3, 0],[4, 0],[5, 0],[6, 0], [7, 0]],
                 [[0, 1],[0, 2],[0, 3],[0, 4],[0, 5],[0, 6],[0, 7]],
                ]
                }} $class;
}

sub get_moves {
    my $self = shift;
    my ($row, $col) = @_;

    return $self->{$row}{$col};
}
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