We should correct ourselves at the outset: the First National Bank building partially survived the Great Fire and was rebuilt shortly thereafter. Designed by Edward J. Burling, a formative Chicago architect from the 1850s to 1890s, the structure at State & Washington came down in the late 1880s to make way for Burnham & Root's Reliance Building. So technically, the place lasted 20 years or so beyond the Fire. The original First National Bank building was built in conjunction with the creation of the First Chicago Bank in 1863, which grew rapidly in the war bonds business. The bank morphed and merged and disappeared in the late 1990s. Gladly many of Burling's post-Fire works, like the landmark Burling Row Houses, live on.
·Hint: An Important Economic Outpost, Lost to the Great Fire [Curbed Chicago]
·First Chicago Bank [Wikipedia]