About 10 minutes into the confrontation, police said, Tiger pulled a gun and fired on the officers. At least one officer fired back, striking him, they said.
"From my view, those three officers are heroes," Allender said. "They were attacked by a guy spraying bullets in their direction. They reacted heroically. They returned fire."
Officer James Ryan McCandless, 28, was killed; Officer Nick Armstrong, 27, was severely wounded and remained in critical condition yesterday. A third officer shot, Tim Doyle, 39, was listed in fair condition, a hospital spokeswoman said.
The three people who were with Tiger have not been charged in connection with the shoot-out.
Allender said some of the officers who were involved are part of the department's street-crimes unit. They had received reports the four people were causing problems, and officers saw them with a bottle of alcohol, the chief said.
"Abruptly, during this contact, the suspect pulled out a concealed gun and fired several rounds at them. It turned into a gunbattle," Allender said.
He said the state Division of Criminal Investigation is looking into the case, but he believes that the three officers had followed proper procedures.
They were wearing protective vests but apparently got shot outside the chest area protected by those vests, Allender said.
McCandless, a six-year police officer, had recently told Allender he had wanted to be police chief when Allender retired. He also was engaged to be married and recently bought a house and a farm where he was raising horses and goats.
He was familiar to many in the area because he appeared on televised public-service spots last year dealing with underage drinking and driving, burglary and other issues.
McCandless was the first Rapid City police officer killed in the line of duty since 1985. The city is on the edge of the Black Hills.