question using aggregate function

I know that:

select max(order_date) from orders;

will return the date of the newest order, and that:

select supplier_id, max(order_date) from orders group by supplier_id;

returns the newest order date from each supplier. But I'm trying to write a query that would return only the supplier_id of the most recently placed order. How would I do that? I thought maybe:

select supplier_id, max(order_date) from orders group by supplier_id having max(order_date) = order_date;

but it complains that order_date isn't a group by expression in the having clause.

Any ideas how to do this?