For now, however, Mills toils far from hockey's brightest lights.
Mills signed last week with the Utah Grizzlies, who open their ECHL season Friday night at Idaho.
A perfect storm of events, including the NHL lockout and Mills' conversion to the LDS Church a few years ago, resulted in a decision that delights his new boss.
"Brad is a huge last-second addition to our team," said Kevin Colley, the Grizzlies' director of hockey operations and head coach. "The opportunity to add a player who spent time in the NHL … is a special circumstance."
A year ago, Mills made New Jersey's season-opening roster. But he split time between the Devils and their American Hockey League affiliate in Albany and never established himself.
"I wasn't a very happy guy it was pretty stressful," Mills said. "At the end of the year I saw where I fit in with the Devils. I realized they didn't see me as a full-time NHL player. So I thought I would try to find another organization."
Mills couldn't have picked a worse time to job hunt.
The ongoing labor war between NHL owners and players has "handcuffed the teams that had expressed interest. … It's really put the squeeze on the number of jobs available."
So Mills started looking around.
Eventually, he talked to Chris Brooks, a former teammate at Yale who previously played for Colley and the Grizzlies.
Brooks "… had a lot of good things to say about the city and the coach," Mills said.
Something else intrigued him about the possibility of playing for the Grizzlies, too.
As a member of the LDS Church, he "started thinking about Utah. … There's not as much of a following back east so I felt like this might be a good opportunity. It was definitely an appealing aspect of playing here."
Mills' short-term goal is helping Colley and he Grizzlies get off to a quick start this season.
Long-term, he's like to parlay his time in Utah into another shot at the NHL.
"Once the lockout is resolved," he said, "my ideal path would be to sign with another team and work my way back to the NHL level."
One problem: Mills believes this labor battle could last a long time.
"As guys start missing paychecks and owners start losing money, the pressure mounts and hopefully a deal gets done," he said. "But my feeling is that's a ways away."