Philosopher of science Jay Richards is a proponent of intelligent design, i.e. the view that the universe and life show evidence (lots of it) of having been intelligently engineered. Richards asserts that one of the most frequent objections he encounters, one raised in fact by Richard Dawkins in his best-selling book The God Delusion is, "If the universe and life are designed then who designed the designer?"
Laypeople can be forgiven for asking the question because it seems common-sensical, but someone of Dawkins' stature should know better and he took a lot of heat from philosophers, even philosophers sympathetic to his metaphysical naturalism, for his evident lack of philosophical sophistication.
Here's a short video in which Richards addresses the question:
It's worth noting, I think, that the attempt to use this question as an indictment of the intelligent design hypothesis is misguided for other reasons besides those Richards gives.
Let's look at the first part of the question: "If the universe and life are designed...." implies a willingness to accept for the sake of argument that the universe is designed, but as soon as he's granted that the naturalist has gotten himself into trouble.
Once it's conceded by the naturalist, even if only hypothetically, that the universe is designed then whether there's just one designer or an indefinite number doesn't much matter. Naturalism would stand refuted since naturalism holds that the universe is self-existent.
Moreover, to posit more designers than what's necessary to explain the universe is a violation of the principle that our explanations should contain the minimum number of entities necessary to explain what we're trying to explain - in this case, the universe. So the simplest, and therefore the best, explanation is that there's only a single designer of the universe. There's no warrant for thinking that anyone who believes there's a designer of the universe must allow for an infinite regress of designers.
We might also point out that the universe is the sum of all contingent entities. Thus, whatever designed the universe cannot itself be contingent lest it be itself part of the universe. Now contingent entities require a necessary being as their ultimate cause and a necessary being is, by definition, not itself dependent upon anything else for its existence. So, if the universe was designed by a non-contingent being then it makes no sense to ask what designed it. Nothing designed it. If it were designed it would be contingent and thus part of the universe.
Finally, it should be noted that if there is an intelligent designer it must not only be a necessary being, but it must also transcend space and time because these are aspects of the universe. Therefore, the designer must be non-spatial and non-temporal. It must also be very intelligent and very powerful. In other words, it must be something very much like God.
Given all this, the naturalist would be better off resisting the temptation to ask "who designed the designer." It's a question which carries far less polemical punch than they think it does.