A bit more reading suggests the Mississippi and the Great Lakes are
connected via Chicago and that there is discussion of re-serarating
the systems to prevent the spread of invasive species Quite a
learning venture. Here is what I found:

Recently, researchers at the University of Illinois at Urbana-
Champaign created a three-dimensional, hydrodynamic simulation of the
Chicago River, which suggested that density currents are the cause of
an observed bi-directional wintertime flow in the river. At the
surface, the river flows east to west, away from Lake Michigan, as
expected. But deep below, near the riverbed, water travels west to
east, toward the lake.[8]

All outflows from the Great Lakes Basin are regulated by the joint
U.S.-Canadian Great Lakes Commission, and the outflow through the
Chicago River is set under a U.S. Supreme Court decision (1967,
modified 1980 and 1997). The city of Chicago is allowed to remove 3200
cubic feet per second (91 m³/s) of water from the Great Lakes system;
about half of this, 1 billion US gallons a day (44 m³/s), is sent down
the Chicago River, while the rest is used for drinking water.[9] In
late 2005, the Chicago-based Alliance for the Great Lakes proposed re-
separating the Great Lakes and Mississippi River basins to address
such ecological concerns as the spread of invasive species.[10]