This is a question that every CCW license holder must ask themselves. Conventional wisdom says carrying a concealed firearm with a round in the chamber will increase the risk of an accidental discharge. If you accidentally catch the trigger on a piece of clothing, it may compress and cause it to fire, potentially injuring you or someone around you.
Playing the Devil's Advocate
On the other hand, carrying your firearm without a round in the chamber could prove disastrous in the event of an attack. Sure, it may only take you a second to pull back the slide of your semi-automatic pistol and ready a round in the chamber, but that second could mean the difference between life and death. If an attacker, who is standing a couple feet away, comes at you, will you be able to draw your pistol, pull back the slide, aim, and shoot in enough time?
Bear in mind that your body will react differently under stress, which may in turn cause you to mishandle the slide. The human body is hard-wired to react differently under stressful situations; your body will produce more adrenaline, your blood pressure will rise, and you'll become jittery. All of these effects can make the otherwise simple task of pulling back the slide of your pistol more complex and difficult. Extensive practice is required to ensure your muscle memory can take over and mitigate these factors.
Is Carrying with a Round in the Chamber Really Safe?
Assuming you are proficient and knowledgeable on how to use your firearm and have a secure holster to carry with, then carrying with a round in the chamber can be just as safe as carrying without a round in the chamber. Some of the older-model pistols from nearly a century ago had a tendency to misfire, but thanks to modern advancements in firearms, there's really no chance of a new pistol discharging unless the trigger is pulled. As long as the trigger remains secure, your gun is safe and won't fire.
A good holster is well worth the investment, it will control and secure the trigger. The holster should cover the trigger guard, maintaining a firm, solid texture that prevents compression. Leather holsters have a tendency to become soft over time, which can increase the risk of an accidental discharge, so be sure to monitor your holster's condition and replace it as needed. Plastic and synthetic materials, on the other hand, typically do not have this problem, but may be more abrasive against skin.
The bottom line is that you can safely carry a firearm with a round in the chamber. As long as you are familiar with your firearm and keep it secured in a good holster, there's virtually no chance of an accidental discharge occurring.
* Image used by creative commons license, credited to Ken.