On private property, including your own driveway or a fenced job site, South Elgin does not publish a permit requirement for the container itself. That covers almost every residential rental here.
The Village also does not publish a street permit for a container. Its forms list covers block parties and temporary street closures, oversized vehicles and business paperwork, but there is nothing for occupying a street or parkway with a container. Because nothing is published either way, the sensible step is to ask before you plan a street drop rather than assume. Call the Community Development Department at 847-741-3894, or email the department through its page on the Village site. The office is at Village Hall, 10 N Water Street.
On a commercial site there is one zoning rule to keep in mind. Permanent refuse and recycling containers are not allowed in the front yard and have to be screened. That rule is written for the fixed containers a business keeps on site rather than a temporary project container, but it is a good reason to plan the drop spot at the side or rear of a commercial lot.
There is also a Village rule about who may collect waste here, and it is worth knowing before you book. For houses and small residential buildings, South Elgin requires owners and occupiers to use the Village's own contracted collection system, and Illinois defines that waste broadly enough to include construction and demolition debris. Buildings with five or more units, and every commercial and industrial property, sit outside that arrangement and deal with a licensed collector directly at a privately negotiated price. Your account manager will work out which side of that line your address falls on and tell you plainly before anything is scheduled.
Before you book, confirm with the city that a container can be placed for your job at your address. Rules differ from city to city and they change. Your Prime Dumpster account manager will help you check, and will tell you plainly what your options are here.