If you mean "at no point in its history did this Earth-sized planet ever have more than one language" then the answer is no.
Languages naturally diverge. There are a number of languages spoken today, called Romance languages, that are all basically 'the local version of Latin, 2000 years later'.
The population required to support a language is relatively small. In Papua New Guinea, there are a very large number of languages, most of which are spoken by fewer than 1000 people.
Also, languages can change gradually -- you can have a bunch of villages where everybody can understand people from the neighboring villages, but not from far away. Say we have villages A, B, C, and D. People from A understand B, and B understands C, and C understands D, but people from A and people from D can't understand each other at all.
To even try to prevent multiple languages from arising at all, we'd need an unrealistically high capability for communication (as soon as the species evolved an ability to speak, but long before they get technology) and an unrealistically low rate of migration and population expansion.
If you mean "could a large civilization divided into many subsections, each with its own language, permanently eliminate all but one of those languages, and prevent the One True Language from splintering into mutually incomprehensible sub-languages" then the answer is not quite no, but almost.
First, they could try force. Say Hitler won WWII and decided to make non-German languages illegal. Trying to do this, though, would take a lot of work, and would likely make most of the conquered territory harder to control. The slight efficiency gain (if it worked) would be outweighed by the problems it caused. Even if it worked, the effort would never go away, because they'd have to keep every dialect of German mutually intelligible.
If you're trying to make your civilization look better than ours because of the single language, the "we slaughtered all the heretics" approach doesn't help.
Second, they could try a vote. Say the UN became the world government and tried to vote on which language would become the official language of the world.
How do you convince, say, the Chinese that despite Chinese having more speakers, the official world language ought to be English, darn it, and I'm not just saying that because I happen to be a native speaker and therefore wouldn't have to learn anything myself. Or French, and it's not because I'm from France and want to increase the prestige of France. Or Japanese, because it's the most beautiful language in the world, and no, that statement is not biased by my being the Japanese ambassador to the UN, it's just true. And so on.
Official languages don't necessarily prevent other languages from being spoken. In Papua New Guinea, which has an enormous amount of linguistic diversity, there are 3 official languages: Tok Pisin, English, and Hiri Motu.
You could try to invent a new language and get people to want to speak it, in the hopes that, not having any native speakers, it would be more politically neutral. This has been tried before, and Esperanto is the most famous and successful attempt at it. Looking at the Wikipedia page, it has various estimates for the number of speakers, the largest of which is 2 million.
That may sound like a lot, but it isn't: English has 232 million in the U.S. alone, German has over 94 million, Dutch 20 million, French has 51 million in France alone, Spanish has at least 280 million, Portuguese over 160 million, Romanian about 20 million, Russian 214 million, Hindi 200 million, Hungarian 14 million, Finnish 5 million, Turkish 45 million, Tamil 48 million, Vietnamese 58 million, and Chinese over a billion.
I'd guess that the probability of Esperanto or any other invented language becoming very widely used as very low, although not impossible. Part of the problem is that if I, a native speaker of X, want to talk to a native speaker of Y, then there are lower effort solutions: I could learn Y, or he could learn X. If we did decide to both spend the effort to learn an entire new language, what advantage is there of learning an invented language with a few speakers over learning a large and popular native language?
If you mean "could I tweak the psychology of my aliens until this would work", then sure.
You just need to figure out how to make the aliens different enough from humans that it becomes plausible. For example, if the aliens reproduce by dividing into two people while keeping all their old memories, they would be 'born' knowing a language, reducing the tendency of languages to change considerably.
There is a misconception I'd like to address in the question: you assume that there is an enormous amount of inefficiency involved in dealing with language barriers, to the extent that we ought to do something about it. Most of the problems can be solved quite adequately with one or more of hired translators, bilingualism, and Lingua Francas. Most of the rest can be solved with creoles, pidgins, dictionaries, and computer programs (like google translate).
If you revise your goal to "everybody on the planet understands language X, and can speak it, more or less", then this is much more easily achieved, and would have very nearly the same communication benefits.