Hundreds of people filled the Boston City Council chambers yesterday afternoon, spilled into first one and then a second overflow chamber to voice their support for or opposition to the Just Cause Eviction proposal currently before the council.

The proposal seeks to ban new building owners from evicting current tenants, and requires landlords to give specific reasons for evictions, including damage to property or nonpayment of rent. Current Massachusetts law allows for “no-fault” evictions, which means landlords aren’t required to provide a reason.

Owners who are Boston residents and whose buildings contain five or fewer units would be exempt from the proposal, if it passes.

A previous version of the proposal requiring that rent increases of 5 percent or more be subject to a nonbinding mediation, but that highly controversial component was recently dropped.

A few dozen advocates – many holding large keys with the names of Boston’s neighborhoods on them – gathered outside City Hall to share their stories of evictions and rising rents immediately before the 4 p.m. meeting.

After demonstrating outside and attending the hearing, Lori Hurlebaus said she hoped the massive “amount of community support not only from renters but from homeowners” would help influence city councilors to support the proposal.

“I grew up here and now I can’t find a home here,” she said. “To me, that’s injustice. This is about having a vibrant wonderful city for all of us.”

Linda Levine, board member of the Small Property Owners Association, was clear and concise when asked what she hoped would happen as a result of the hearing.

“Actually we’re hoping nothing will happen,” she said. “We’d like to think this proposal is going to go nowhere.”

The council is scheduled to discuss and possibly order a hearing on Just Cause Eviction at the next meeting on Wednesday, March 16.