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In the 1920s, as the Washington Heights community area was experiencing a building boom, the Fernwood Park District decided to create a new park before it was too late to acquire vacant land. Serving a neighborhood that was once the old Village of Fernwood, the Fernwood Park District had formed in 1908. In 1925, after canvassing local property owners on the most desirable park location, the district acquired a site for the park. Although there were limited funds for improving the property, the local community helped out. As ballfields were being laid out in 1926, the Fernwood Community Association donated lumber for the back-stop. The park was expanded again after the Fernwood Park District acquired more land in 1929.  An area real estate office structure was moved into the new park for use as a small recreation building.

Originally named Fernwood Commons, the site likely became known as Euclid Park to avoid confusion with nearby Fernwood and Fernwood Parkway Parks. Making reference to the ancient Greek mathematician who wrote the "Elements," Euclid Park's name was derived from the surrounding subdivision, O'Dell's Addition to Euclid Park.

In 1934, Euclid Park became part of the ¿ì²¥ÊÓƵ when all 22 of the city's independent park commissions were consolidated into a single agency. After improving the park's landscape and adding tennis courts, the newly-formed park district began offering glass blowing, model airplane-making, and other crafts classes in Euclid Park's small building. In 1960, the park was fully rehabilitated and its original structure was replaced with a new fieldhouse. In the in 1961, a portion of 98th Street was vacated for parkland.  The City of Chicago created the Euclid Park Connector by vacating a portion of South Wallace Avenue into greenspace to provide an attractive and safe connection between Medgar Evers Elementary School and Euclid Park.