The award is given annually to the NHL's best defenceman.
Chara, who won the award in 2009, is a finalist for the sixth time.
The Bruins captain had 17 goals and a plus-25 rating this past season.
Keith finished first among defencemen in assists with 55 and second in points with 61. He won the Norris in 2010, the only other time he was a finalist.
Weber, the captain of the Predators, had 33 assists and led all blue-liners with 23 goals. He was a finalist in 2011 and 2012 but has never won the award before.