Ammo
Contrary to popular misconception, .223 (for example, American Eagle) and 5.56mm (XM193*) are not the same cartridge. The SAAMI spec for .223 is shorter than the 5.56mm. While .223 ammo can be safely fired in 5.56mm chambers, it is not generally safe to fire 5.56mm ammo in .223 chambers since the bullets can be longer and actually jam into the rifling.
In addition, the SAAMI pressure spec for .223 is lower than the mil spec for 5.56mm. The SAAMI web site advises that 5.56mm is unsafe in a .223 chamber.
It's generally a bad idea to get a .223 SAAMI chamber unless you are going to be careful to use only .223 ammo, or load your own to SAAMI dimensions. In addition to the mil spec 5.56 chamber, there are various other chambers designed to accomodate both cartridges - for example, the Fulton Armory "5.56 match" chamber, or the Wylde chamber used by vendors such as JP Rifles.
Google ".223 5.56 differences" for details.
* - The XM193 on the civilian market is generally thought to be surplus which either did not pass mil spec testing, was part of a batch where some did not pass, or was not qualified and documented as such. It's still good stuff though.