Architect Daniel Burnham, whose fingerprints are all over so much of modern Chicago, famously advised, “make no little plans; they have no magic to stir men’s blood and probably themselves will not be realized.”

That, in a proverbial nutshell, is Chicago at its finest: daring to dream and willing to put in the effort to make those dreams reality — whether that means establishing a trading post atop a marsh, rebuilding after a legendary, catastrophic fire or fashioning an iconic skyline that stretches halfway to the heavens. The photos LIFE.com selected to kick off its “Great Cities” series perfectly capture the fully realized dreams of the men and women of Chicago, and epitomize why the 20th century was, so emphatically, “The American Century.”

Passion — daring to dream — permeates the town and, in large part, defines Chicagoans, both native-born and adopted. This is the city that gave us Nelson Algren, Studs Terkel, Gwendolyn Brooks, Carl Sandburg, Roger Ebert, Mike Royko. Chicago is where Oprah Winfrey and Michael Jordan became global superstars. It is the birthplace of the Temperance movement — and it’s where booze flowed like water during Prohibition. Over the decades, its politicians and mobsters have often been indistinguishable from one another, while Chicago’s struggles with poverty, violence and political corruption — like those of any other great, international metropolis — are as old as the city itself.

In the end, though, Chicago’s well-documented woes are as much a part of the city’s fabric as its glories, its triumphs, its world-class cultural achievements.

Daniel Burnham also wrote, “aim high in hope and work, remembering that a noble, logical diagram once recorded will not die, but long after we are gone be a living thing, asserting itself with ever-growing insistence.” Those of us who call ourselves Chicagoans continue to dream big, to reach higher, hoping to add our names to the city’s bold, forever unfolding narrative — and inspire the dreams of future generations in the city we love.