A woman is driving dangerously down a winding road, recklessly passing cars until she comes upon a slow moving Mack truck. As she goes to pass, her car is clipped by a truck going in the opposite direction, then slammed full-force by the Mack, killing her.
Meanwhile, John Quincy Archibald and his wife Denise witness their young son Michael collapse at his baseball game and take Michael to the hospital. After a series of tests at the hospital, John is informed by Dr. Raymond Turner and Rebecca Payne, the hospital administrator, that his son has an enlarged heart and will need a heart transplant to live. The procedure is very expensive: $250,000 (at a minimum), with a down payment of $75,000 (30%) required to get Michael's name on the organ donor list. John tells them he is insured, but after looking through his policy, they tell him that because the company he works for dropped John from full-time to part-time, his health insurance has been changed, and the new policy does not cover the surgery, which leaves John and Denise to raise $75,000 on their own. The family tries to raise the money but are only able to come up with a third of the necessary payment. The hospital tires of waiting and releases Michael; Denise urges John to do something. Unwilling to let his child die, John walks into the hospital ER with a handgun, gathers eleven hostages, and sets demands: his son's name on the recipient list as soon as possible. The hostage negotiator, Lt. Frank Grimes, stands down to let John cool off.
Meanwhile, John and the eleven hostages learn more about each other. They begin to understand John's situation and support him a little as he ensures each of them receive the treatment they came to the emergency room for. One of them, Miriam, is pregnant, and her husband Steve is hoping that their first child is healthy. A young hostage, Julie, has a broken arm, and she and her boyfriend Mitch claim that a car crash caused it. Due to holes in their story, John and another hostage, Lester, conclude the two are lying and that Mitch beat up Julie. After a while, John agrees to release some hostages to have his son's name added to the list an hour afterward. He releases Steve, Miriam, and a hostage named Rosa with her baby.
The Chicago Chief of Police, Gus Monroe, gives a SWAT unit permission to insert a sniper into the building via an air shaft. John is shot but ends up receiving only a minor wound, which is treated right away. After taking the shot, the sniper's leg falls through the ceiling tiles. Outraged, John pulls him out of the air shaft and beats him up. Using the bound SWAT policeman as a human shield, he steps outside to the sight of dozens of policemen pointing weapons at him and a large, supportive crowd. John demands that his son be brought to the emergency room. The police agree to his demand in exchange for the SWAT sniper.
Once his son arrives, John reveals to the hostages his intention to commit suicide so his heart can be used to save his son. He persuades Dr. Turner to perform the operation, and two of his hostages bear witness to a will stating his last request. John says his last goodbyes to Michael and enters the operating room. He loads a single bullet into the gun and pulls the trigger, but the safety is on. As he prepares to end his life a second time, his wife learns about an organ donor (which happens to be the female driver that was killed in the beginning of the movie) who has been flown to the hospital for organ recovery. She runs to the emergency room and stops John from shooting himself, and John allows the hostages to go free. Michael is given the life-saving operation and, after watching the procedure with Denise, John is taken into police custody. Afterwards the entire ordeal becomes subject to a national debate about the quality and accessibility of insurance and healthcare. Three months later at his trial, all of the witnesses speak on his behalf. He is later acquitted of charges of attempted murder and armed criminal action but is found guilty of kidnapping. It is never revealed what his sentence for the crime will be, but his lawyer is overheard and saying that no judge will give him "more than three to five (years)" and that she will try to get it reduced to two.

Question: What did Chief of police gave SWAT permission to do?
Answer: Insert a sniper into the building air shaft.
Alternative answer: to insert a sniper into the building via an airshaft to take John down