Numerous examples in older parts of the city can still be found paved with Belgian wood block from the late 19th and early 20th century. However, before Belgian block became common, there were many different pavement methods with wildly varying advantages and disadvantages. Because it was so cheap wood block was one of the favored early methods.
The wood block pavement was more commonly known as Nicolson pavement, which Chicago started using by 1853.
In the landmark Astor Street District in Chicago's Gold Coast community, the alley between State and Astor Streets, less than a block south of North Avenue, behind the mansion of the Archbishop of Chicago (1555 North State Parkway), is a wood block alley running east and west.
In May of 2011, the Gold Coast wooden alley was torn away and replaced with new wooden blocks.
I personally cannot verify this, but a second wood block alley is said to be between the 1900 block of North Hudson and North Cleveland Avenues.