This question is almost impossible to answer precisely through counting, as Chicago is so large and constantly changing that you might encounter a “counting heads in China” problem: the exact figure is changing faster than you can count it practically by hand.
However, one can approximate the number of city blocks by figuring a rough average for the length of a city block in each direction, then multiply that figure by the length and width of the city area to get a reasonable estimate. Downtown Chicago has city blocks that are close to 250 feet in length both longitudinally and latitudinally, or around 80m, for a city block parcel of 640 m^2. The entire city of Chicago occupies an area roughly 20 km north-south by 10 km east-west, for a total area of some 200 million m^2. Dividing the total area by the average area per city block yields a final figure of some 312,000 total city blocks. I performed this calculation using the Google Earth search below; you can replicate the process if you want to do a more precise calculation.
Alternatively, with GIS software such as ArcGIS (see 2nd link below), along with a map of Chicago, a good scanner, and a steady hand, you could calculate the exact number of city blocks, so long as the map remains accurate.
I could not find any exact number of blocks, but I believe this can be answered using arithmetic. Chicago is 228 sq. miles. Each mile contains 8 blocks. Thus, 8 x 228 = 1,824 blocks.
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