The governor says the law will prevent a community's political make-up from being weakened by dividing into multiple voting districts.
Chinatown is one such community. It is currently divided into four parts of city wards and three state senate districts.
"We know we have to be fair when districting or remapping. Everyone's given a fair chance when electing senators and congressmen of their choice. That's all of our mission," said Quinn.
The new law also means the legislature now must hold four public meetings before it can pass any future redistricting plans.