Johnson, 24, was serving 8 1/2 years for first-degree burglary in Carroll County, Gelsinger said.
Maryland State Police and other local law enforcement officers were looking for the men. A state police helicopter and a police K-9 unit were helping with the search.
Maryland Correctional Training Center is one of three state prisons in a complex on Roxbury Road south of Hagerstown.
The men did not climb over a fence, said Mark Vernarelli, a spokesman for the Maryland Department of Public Safety and Correctional Services, which includes the state prison system.
Police described Chait as a white man, 5 feet 7 inches tall, weighing 175 pounds. He has tattoos on his neck and arms.
Johnson was described as a white man, 5 feet 11 inches tall, weighing 186 pounds.
Both were wearing white jumpsuits.
Gelsinger said Chait was to be released in early 2012 and Johnson in the middle of 2011.
They were in a "pre-release status," according to the state police news release.
Gelsinger said the escape was discovered at 10:50 a.m. Ten minutes later, a formal count was taken to determine which inmates were gone.
A siren was sounded to alert the neighborhood, according to Vernarelli. A neighbor who lives on Sharpsburg Pike near the prison entrance confirmed she heard the siren at about 11:40 a.m.
But Kevin Damewood, who lives on Barnes Road, about one or two miles from the complex, said he was home starting at 10:45 a.m. and didn't hear it.
"Unless I'm deaf, I am not hearing any siren," he said.