Don't confuse chrome lining with chrome moly. Most AR15 barrels are "chrome moly", it has nothing to do with chrome lining though.
There is no reason not to chrome line your chrome moly barrel if your number one concern is reliability. Some manufacturers charge $30 or so for chrome lining. Other manufacturers chrome line their barrels standard.
The 5.56/.223Rem cases are not tapered much at all so the case makes contact with the chamber for much of the feeding and extracting. That is why it is so imperative that your chamber stays clear of corrosion, rust, and pitting. This was a lesson that was quickly learned by the military when it rushed the M-16 into service in Vietnam.
William Davis, Former Chief, Small Arms Branch recalled that, “The principle problem was a failure to chrome plate the chamber. That was the cause of the serious malfunctions that caused the controversy in Vietnam.”
Chrome will also make the chamber more “slick” than steel, which will enhance feeding and extracting.
Chrome lining increases the life of your barrel because it is harder than steel. It will ease cleaning and maintenance as well.
The one downside to chrome is an ever so slight decrease in accuracy in some cases. This difference in accuracy is practically unnoticeable and will not be missed in a defensive weapon. However, when done properly by a quality manufacturer, no accuracy will be lost.
Your chrome moly barrel should be chrome lined in a serious rifle, regardless of whether it is 4140 or 4150. Go chrome or go home.