Both must be confirmed by the state Senate for their new roles.
The Republican governor said he hopes Chiesa can be confirmed before Jan. 1. When that happens, Dow would move to the Port Authority of New York and New Jersey to serve as the first deputy general counsel while she awaits confirmation to the bench.
Both Dow and Chiesa are original members of Christie's administration and have served in their respective roles for about two years.
Dow, a Democrat who served as Christie's counsel for a year when he was U.S. attorney, does not need confirmation for her role at the Port Authority. Christie said she will "quickly recommend structural and procedural changes that will end the abuse and waste that has marked the authority's past."
Dow said the bistate agency "needs a lot of attention at this time."
Christie said he expected a quick confirmation for Dow, because she has been through it before.
"There can't be any dispute over this," Christie said, noting that she has already been twice confirmed by the Senate for her previous two jobs as Essex County attorney, then as attorney general.
Chiesa has known the governor for more than 20 years and served as executive director of Christie's transition team. He previously was a partner at the law firm of Wolff & Samson in their litigation group and before that worked in the U.S. attorney's office.