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 commonsensical, 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 the naturalist grants, even if only hypothetically, that the universe is designed he gets himself into trouble.
Whether there's just a single designer or an indefinitely long chain of designers doesn't much matter. Naturalism would stand refuted since naturalism holds that the universe is self-existent.
Moreover, to posit more causes/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.
The simplest, and therefore the best, explanation is that there's only a single designer of the universe. There's no reason to think that the belief that the universe is designed entails an absurdity like an infinite regress of designers.
We might also point out that the universe is a contingent entity. It could possibly not exist. Now contingent entities require a necessary entity as their ultimate cause, and a necessary entity is, by definition, not itself dependent upon anything else.
Thus, if the universe is ultimately the product of a necessary or non-contingent being then it makes no sense to ask what designed the non-contingent being. Nothing designed it. If it were designed it wouldn't be a necessary being, it'd be contingent.
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 the universe. This means it must transcend space, time and matter because these are aspects of the universe. Therefore, the designer must be non-spatial, non-temporal and immaterial. It must also be very intelligent and very powerful to design and bring into being a universe.
In other words, it must be something very much like God.
Given all this, the naturalist would do better to resist the temptation to ask "who designed the designer." It's a question which carries far less polemical punch than they think it does.