CHICAGO (CBS) — For the first time, the city’s top doctor is letting us all pull out some calendars.

City officials tentatively plan to be able to make the COVID-19 vaccine available to everyone in Chicago by May, and are hoping to soon be able to resume indoor dining at restaurants and bars after other COVID-19 restrictions in Chicago were lifted on Monday.

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Chicago Department of Public Health Commissioner Dr. Allison Arwady discussed the details of the city’s vaccination plans during her regular “Ask Dr. Arwady” livestream on Tuesday, but she cautioned the scheduled vaccine rollout is “purely speculative” based on how much vaccine the city is getting from the federal government.

Arwady said the city is currently receiving approximately 34,000 first doses of the vaccine per week.

Meanwhile, as CBS 2’s Chris Tye reported, some people who are not yet eligible for the vaccine have been getting it anyway at Walgreens stores, due to a reported glitch in the system. CBS 2 reported on that issue Monday night.

“It was a relief,” said Terry Abrahamson. “It was great.”

Terry and Vicky Abrahamson of Chicago don’t work at a hospital or assisted care facility, but they got vaccinated at a West Wide Walgreens on Tuesday.

The drugstore’s corporate website had several Chicago locations open for appointment vaccines Tuesday. But the Abrahamsons made their appointment last week in what they think was a glitch in the Walgreens system.

“It didn’t ask if you were a health care worker. They sent the wrong questions out. If you went on it later, it asked if you were a health care worker. We already had our appointment at that point,” Vicky Abrahamson said, “They honored it.”

You won’t need a glitch to make an appointment starting next Monday.

Arwady said Chicago will move into Phase 1B of virus distribution on Monday, along with the rest of the state. During Phase 1B, vaccines will be available to people 65 and older; non-healthcare frontline essential workers such as police officers, firefighters, correctional workers, teachers, grocery store workers, public transit and postal workers, and daycare, K-12, and early education workers; and non-healthcare residential settings such as jails.

The city tentatively plans to begin Phase 1C at the end of March, and to launch Phase 2 at the end of May.

During Phase 1C, all other essential workers and anyone between 16 and 64 years old with an underlying medical condition would qualify for the vaccine. During Phase 2, everyone in Chicago age 16 and older can get a vaccine.

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Arwady said it’s unlikely children under age 16 will be able to get the vaccine until this summer at the earliest, as they weren’t included in the original trials of the existing vaccines, and experts are still working to determine if they’re safe for children.

To get updates on when and how you can receive a vaccine, you can sign up for the city’s Chi COVID Coach system.

Meantime, Arwady and Mayor Lori Lightfoot said they hope Chicago restaurants and bars can resume indoor service soon.

On Monday, Gov. JB Pritzker’s office announced Chicago had moved to Tier 2 of the state’s COVID-19 mitigation efforts, allowing for gyms and fitness centers to reopen at 25% capacity and to resume group fitness classes (with masks and social distancing required), for the return of lower-risk youth and recreational sports, and for the reopening of museums, theaters, and other cultural institutions at 25% capacity.

“I’m glad that the change is made to open up the possibilities for our museums and gyms to be able to open up at limited capacity, and I’m looking forward to a day when we, and hopefully soon, see indoor dining in restaurants,” Lightfoot said at an unrelated event Tuesday morning in Chatham.

To move to Tier 1 restrictions, which would allow for the return of indoor dining, Chicago must reach a 7-day average test positivity rate below 8% for three days in a row, have at least 20% of its intensive care unit beds available for at least three consecutive days, and have no sustained increase in COVID hospitalizations for 7 of the past 10 days.

While Chicago already meets the hospital benchmarks, it hasn’t quite reached the required positivity rate. As of Tuesday, the city’s 7-day average test positivity rate stands at 8.1%.

Arwady said it’s possible Chicago could meet the requirements to roll back to Tier 1 mitigations by this weekend or early next week if current trends hold.

Lightfoot also said she’s hopeful indoor dining will resume soon.

“We are definitely trending in the right direction today,” Lightfoot said. “We’re still seeing too many cases, and we’re absolutely seeing too many deaths. The tragedy of this pandemic unfortunately continues, but there’s hope at the end of this long journey, but we’ve got to be remain diligent, but I’m optimistic that we’ll see indoor dining in restaurants relatively soon.”

As to the issue at Walgreens with ineligible people getting vaccines, the company released a statement late Tuesday reading: “We are looking into the matter and are taking additional steps to ensure eligible individuals are receiving the vaccine.”

CBS 2’s Chris Tye contributed to this report.

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