The Housing Committee could vote on the mayor's Protecting Renters Ordinance or PRO.
Supporters said it cracks down on predatory practices by landlords.
The plan introduced this summer, would establish "just cause" before landlords can evict tenants.
A key provision in the original proposal also requires landlords to provide relocation assistance depending on why the tenant is being asked to move.
But the initial amount of up to $10,000 may have been adjusted to get the provision passed.
Mayor Johnson said an update to the renters' ordinance is long overdue.
This ordinance has not been updated in 40 years since Mayor Washington initiated this charge to provide better protection of the city of Chicago. Fifty four percent of the residents of our city are renters There were concerns that were brought to me by landlords, smaller landlords in particular, that we took into serious consideration.
Opponents said the mayor's plan puts and undo burden on small landlords and would result in higher rents.
A coalition of aldermen are pushing for a competing ordinance called FAIR. It redefines small landlords, doubles the number of units they can own from 6 to 12, and eliminates the requirement they live in the building they are renting.
The PRO is scheduled to come before the Housing Committee Wednesday, while the competing FAIR ordinance will be heard Thursday in the Zoning Committee.
Both would need to advance out of committee before being voted on by a full City Council.