Epicurus was a fairly prominent Greek philosopher (founder of the philosophical school of Epicureanism) of the 4th-3rd centuries BCE. The doxographer Diogenes Laertius records a letter from Epicurus to Herodotus, in which Epicurus says [Loeb translation]:

Moreover, there is an infinite number of worlds, some like this world, others unlike it. For the atoms being infinite in number, as has just been proved, are borne ever further in their course. For the atoms out of which a world might arise, or by which a world might be formed, have not all been expended on one world or a finite number of worlds, whether like or unlike this one. Hence there will be nothing to hinder an infinity of worlds.

The idea of infinite worlds is a well-known Epicurean theory, also found in the Epicurean poet Lucretius (1st century BCE) in his epic poem De rerum natura (On the Nature of the Universe) [Loeb translation]:

Now since there is illimitable space empty in every direction, and since seeds [atoms] innumerable in number in the unfathomable universe are flying about in many ways driven in everlasting movement, it cannot by any means be thought likely that this is the only round earth and sky that has been made, that all those bodies of matter without do nothing: especially since this world was made by nature, and the seeds of things themselves of their own accord, knocking together by chance, clashed in all sorts of ways, heedless, without aim, without intention, until at length those combined which, suddenly thrown together, could become in each case the beginnings of mighty things, of earth and sea and sky and the generation of living creatures. Therefore again and again I say, you must confess that there are other assemblages of matter in other places, such as this is which the ether holds in greedy embrace

Besides, when abundant matter is ready, when space is to hand, and no thing and no cause hinders, things must assuredly be done and completed. And if there is at this moment both so great store of seeds as all the time of living existence could not suffice to tell, and if the same power and the same nature abides, able to throw the seeds of things together in any place in the same way as they have been thrown together into this place, then you are bound to confess that there are other worlds in other regions and different races of men and generations of wild beasts.

It is also referred to briefly in Cicero's De natura deorum (On the Nature of the Gods), in the mouth of an Epicurean spokesman [Loeb translation]:

For he [Epicurus] who taught us all the rest has also taught us that the world was made by nature, without needing an artificer to construct it, and that the act of creation, which according to you [Stoics] cannot be performed without divine skill, is so easy, that nature will create, is creating and has created worlds without number. You on the contrary cannot see how nature can achieve all this without the aid of some intelligence, and so, like the tragic poets, being unable to bring the plot of your drama to a denoument, you have recourse to a god; whose intervention you assuredly would not require if you would but contemplate the measureless and boundless extent of space that stretches in every direction, into which when the mind projects and propels itself, it journeys onward far and wide without ever sighting any margin or ultimate point where it can stop. Well, then, in this immensity of length and breadth and height there flits an infinite quantity of atoms innumerable, which though separated by void yet cohere together, and taking hold each of another form unions wherefrom are created those shapes and forms of things which you think cannot be created without the aid of bellows and anvils, and so have saddled us with an eternal master, whom day and night we are to fear; for who would not fear a prying busybody of a god, who foresees and thinks of and notices all things, and deems that everything is his concern?

Edit: typos