However, 9th Ward Ald. Anthony Beale said the plan was a "bad idea" that would waste taxpayer money.
"We should use this money to help people get state IDs," Beale said. "This is also a waste of time and a waste of effort."
City Clerk Anna Valencia touted the card as a way to help those who cannot otherwise get a government-issued identification card to access city services, cultural institutions, programs and other benefits.
The full council is expected to consider the program Wednesday.
Ald. Nichloas Sposato (38th) said he could not support the effort.
"This is the job of the state," Sposato said.
In December, Sposato left the council's Progressive Caucus because of the group's support for several immigrant rights measures, including a $1.3 million fund to defend undocumented immigrants from deportation.
However, other aldermen said the identification card would help city officials protect the most vulnerable residents of the city.
"This is the start that people need," said Ald. Ray Lopez (15th.)
Ald. Marty Quinn (13th) said he would support the cards to be used to give Chicago residents priority for park facilities and programs.
"That is a big issue for my ward," Quinn said.
Valencia assured aldermen she would do everything possible to ensure that the information provided by undocumented immigrants to city officials would not be used by members of President Donald Trump's administration to deport people here without permission.
Ald. Pat Dowell (3rd) said she thought the effort was premature, since it was unclear what steps the Trump administration planned to take regarding undocumented immigrants.
To eliminate that possibility, the city will not keep applicants' addresses and phone numbers on record nor will they keep copies of any documents, according to the measure, which must be approved by the full City Council. It is modeled on San Francisco's policy, Valencia said.
Beale, Dowell, Sposato and 7th Ward Ald. Greg Mitchell abstained from the vote on the measure.
With $1 million earmarked for the city ID program in this year's budget, Valencia said she expects the first card to be issued before the end of 2017.
City officials have yet to determine what documents applicants for the identification card will need to present beyond their names and dates of birth. Officials have also yet to say whether there will be a fee for the card, but the law introduced Wednesday would allow one to be charged.
Applicants will also be able to self-designate their gender in response to concerns from members of the transgender community.
In response to concerns voiced by Ald. Jason Ervin (28th), each card will have an unique number as well as security features to prevent fraud, Valencia said.