But the career policeman Alkhanov faces a battle to garner some of the standing enjoyed by his hard-nosed predecessor Akhmad Kadyrov, assassinated in May, and to bring stability to a region where separatists are becoming more audacious in their attacks.
"I feel an enormous burden of responsibility," Itar-Tass news agency quoted him as saying after the first returns from the polls appeared. "I feel no euphoria. There is a clear understanding that a lot of hard work is ahead."
The poll took place against a backdrop of heavy fighting in Chechnya and two plane crashes that killed at least 89 people elsewhere in Russia.
Investigators say traces of explosives were found on both planes, and many Russians blame Chechen separatists for the disasters.
On Sunday, a man identified as a wanted Chechen rebel was killed by his own bomb near a polling station in the capital, Grozny. He had tried to enter the polling station but while running away triggered the device, an election official said. No one else was hurt.
Separatists assassinated Kadyrov in a May bomb attack that showed the precarious nature of Russian rule. They have vowed to kill Alkhanov as another "Moscow stooge".
"Like last time, the authorities will be signing the death warrant of the man they pick. Neither elections, nor Russia's current politics in Chechnya will bring the desired results," rebel envoy Akhmed Zakayev said in a recent statement.
Tens of thousands were killed in the first Chechen conflict from 1994 to 1996. Putin sent troops back into the mainly Muslim territory on Russia's southern fringes in 1999 to cement his image as a strong leader ahead of his own election.
But victory over the rebels has eluded Putin, now in his second term, and the killing of Kadyrov – Putin's iron man in the region – was a major blow. He now is looking to the tall, moustachioed Alkhanov to do what some say is the impossible.
Alkhanov told Tass he saw no prospects for talks with the rebel leader Aslan Maskhadov or any of unrepentant guerrillas. "They can stage explosions and kill, but the will of the people has already thrown them out to the history dump together with Maskhadov," he said.
Chechnya's economy has been shattered by war. As much as 70 percent of the population is unemployed and the role the region once enjoyed as a transit route for oil was destroyed by violence and corruption years ago.
Alkhanov said that apart from ensuring security for Chechens, his administration would focus on reviving Chechnya's economy and creating 150,000 new jobs in the next five years.
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