He warned scientists not to try to communicate with extraterrestrials, pointing out that, "We only have to look at ourselves to see how intelligent life might develop into something we wouldn't want to meet."
Prof Hawking's concern is shared by others in the field.
They don't object to passive SETI: it can't do any harm to "Search for Extra-Terrestrial Intelligence" by listening with radio telescopes for the radio emissions of civilisations around other stars.
However, they think that active SETI sending out messages saying "Here we are" is just asking for trouble.
"Active SETI ... is a deliberate attempt to provoke a response by an alien civilisation whose capabilities, intentions, and distance are not known to us," wrote Michael Michaud, former Deputy Director of the Office of International Security Policy in the United States State Department, in 2005.
The recent discovery of at least 400 planets orbiting nearby stars makes the issue more urgent, for we now know that planets are common in our galaxy.
There have already been attempts at active SETI.
In 1974, Frank Drake, the astronomer who founded the SETI project, used the Arecibo radio telescope to beam a message towards the globular star cluster M13, which has over a million stars in it.
But M13 is 25,000 light years away, so we have at least 25,000 years to prepare for any response to the message.
In 2008, however, a high-powered message was sent to the Gliese 581 system, a five-planet system that is only 20 light years away and has two planets in the habitable zone for life.
The message will get there in 2029.
Several messages have been beamed to other nearby planetary systems since then, in the blithe assumption that anybody there will be friendly.
Scientist and author Jared Diamond has said that "those astronomers now preparing again to beam radio signals out to hoped-for extraterrestrials are naive, even dangerous".
Mr Michaud was equally concerned, warning that "an Active SETI signal ... might call us to the attention of a technological civilisation that had not known of our existence.
We can not assume that such a civilisation would be benign, nor can we assume that interstellar flight is impossible for a species more technologically advanced than our own."
One assumption embedded in all these warnings is obvious: that life and even intelligence are probably quite common in the universe.
But the other implicit assumption, made even by an outstanding theoretical physicist like Prof Hawking, is that light-speed or faster-than-light travel may be possible.
If it isn't, then there would be little reason to worry about hostile aliens.
They would have no conceivable motive to engage in interstellar raids or conquest, or even interstellar trade, if travel between the stars takes hundreds or thousands of years.
Our current knowledge of physics says that faster-than-light travel is impossible, but leading scientists in the field clearly believe that today's physics may not have the final answers.
We will have to leave that question open for a while, but there are two ways to test the assumption that life is common in the universe.
It will be several decades before we can go to Mars and the moons of Jupiter and Saturn to see if life exists (or once existed) there, but if life really starts up almost anywhere that conditions are suitable, then it's unlikely that it would have emerged just once here on Earth.
All the familiar forms of life on Earth have the same biochemical makeup, which points to a single, common ancestor.
But the vast majority of species on this planet are microbes, and we have scarcely begun to explore their diversity.
Among them there may be species that have a different biochemical basis, perhaps living in isolated parts of the biosphere, or maybe even co-existing with mainstream life.
If we ever found microbes of a different biochemical lineage, we would know that life here has arisen more than once.
If so, then it's probably as common as dirt all across the universe.
If we find no alien microbes, on the other hand, we still cannot be sure that life on Earth is unique, for one theory holds that life is spread from planet to planet, and even from star to star, by asteroid collisions.
Maybe we only had one collision.
There is another way to test for extraterrestrial life.
As our ability to examine the atmospheres of planets circling other stars improves, we should eventually be able to detect the characteristic changes that abundant life of our kind causes in an atmosphere.
Failing to find those changes would not be definitive proof that life is very rare in the universe, but it would be a very strong indication.
In the meantime, maybe it would be wiser not to go looking for trouble.
As astronomer Zdenek Kopal said 20 years ago: "Should we ever hear the space-phone ringing, for God's sake let us not answer, but rather make ourselves as inconspicuous as possible to avoid attracting attention!"
Gwynne Dyer is a London-based independent journalist.
