Trafficking Reduction And Criminal Enforcement (TRACE) Act This bill modifies provisions related to firearms tracing. First, the bill directs the Department of Justice to promulgate regulations that require each firearm manufactured in the United States to be marked with a serial number that is located inside the firearm's receiver or that is visible only in infrared light, in addition to the serial number mark otherwise required. Next, it requires National Instant Criminal Background Check System records to be maintained for at least 180 days. The bill also requires each licensed firearms dealer to conduct a physical check of their firearms business inventory. Finally, it removes limitations on the use of firearms tracing data by the Bureau of Alcohol, Tobacco, Firearms and Explosives.