Quite safe, actually. Here’s a parallel to think about:
First, posit that statistically you can count on the holder of a concealed handgun license (CHL) not to intentionally commit murder; after all, they have all been thoroughly checked out by a background check, and have had some training, etc. Therefore, your main concern is protecting against accidents.
Compare the relative safety of guns versus cars. Every single time you pass an oncoming car on a two lane road, you are within a few feet of a head on collision that could easily kill everyone in both vehicles. Therefore the potential for real tragedy is really very high. Your safety depends entirely on your skill and the skill of the other driver, which varies from nonexistent to professional.
In the case of the CHL licensee, think about this. The skill level required is similar to that required to drive a car. But, note this: the gun in a proper holster is TOTALLY SAFE as long as it is still in the holster. It is the same as your car being completely safe as long as you leave it parked. The skill level / practice / knowledge factor only comes into play if the gun is drawn. Furthermore, it is illegal to draw that gun (in public) unless lethal force is required for defense. It is illegal even to show it – that is called ‘brandishing’.
Just as with cars, it is illegal to carry a gun while mentally impaired by alcohol, drugs, or anything similar. I don’t have statistics, but judging by those I know personally, I suspect the average CHL licensee takes this aspect much more seriously than does the average person driving a car.
Cars can do much more damage in a single act of driver inattention than a gun-toting person can do with an accidental discharge, because car accidents can (and frequently do) kill or injure several people at once; whereas, the accidental discharge of a firearm may or may not hit anybody. If it does, that person probably stops the bullet. It is therefore unlikely that more than one person will be hurt by a single accidental discharge. So, in any single incident, cars are likely to hurt / kill more people than a single accidental discharge of a firearm.
Here’s the kicker, though. That single moment of inattention is far more likely to happen to someone driving a car, because you are in that situation so much more frequently. Again, the gun-toter simply cannot have an accident unless he’s got his gun out of his holster.
I carry every day, everywhere it is legal for me to do so. How much time do I actually have my gun in my hand during an average day? About 30 seconds; I change holsters twice a day (I use a different rig at home than I do in public). How much time do I spend facing other drivers every day? A dead minimum of about 45 minutes.
So – 30 seconds of paying attention versus perhaps 45 minutes of paying attention, to prevent an accident. Which is more likely to produce a mistake? And, the consequences of a mistake are much higher in cars than guns.
Guns are WAY safer than cars. Specifically addressing the context of legal concealed carry.