On private property, including your own driveway or a fenced job site, McHenry asks for no container permit. In fact the City's own rule points the other way: it bars placing refuse on public or private property anywhere in the City unless it is in proper containers for collection, or with the express approval of the Director of Public Works. A properly placed container is the compliant answer rather than the problem.
The street needs authority. It is unlawful to cause or maintain any obstruction of a street, alley, sidewalk or other public way except as specifically authorised by ordinance or by the Director of Public Works, so that office is the route for a street position. The code also sets out what happens when material does sit in a street: the usable width of the roadway may not drop below eighteen feet, anything left after sunset has to be guarded by lights, and material other than material to be used in actual building construction cannot stay for more than three hours.
The sidewalk is tighter still, and it is the shortest limit we see anywhere. An article may be left on a sidewalk only while a delivery is actually happening, the usable width may not fall below four feet, and nothing may remain for more than half an hour. In practice that closes the sidewalk to a standing container.
One McHenry rule is unusually good news and it is worth stating plainly. The City's scavenger licensing chapter does not apply to anyone in the business of construction or trucking who removes, hauls and disposes of building debris, construction debris or junk. It goes further: the City issues only one scavenger license, for one to four family residence service, and says that all other scavenger services in the City are not required to obtain one. So roll-off work for a remodel, a tear-off or a cleanout sits outside that chapter, and its airtight-cover vehicle requirements are keyed to licensed scavengers rather than to us. Your account manager can confirm how it reads for your particular job and will handle the Public Works contact if the street is the only option.