On 21 February 2016, the above-reproduced Facebook photo of Chicago's Trump Tower was shared with the following comment:
Trump challenged Chicagoans by putting his name up on the tower standing mid downtown chicago. For months I drove by and cringed every time I saw his name near the Michigan and Wacker intersection. In response to his selfishness Chicagoans decided to show who they are NOT voting for: — feeling satisfied at Downtown Chicago.
The display apparently caught neither the attention of social media at large (which would have produced a number of shots from other angles) nor the news media, despite its proximity to Trump's win in South Carolina.
That alone made the claim dubious, but a reverse image search located a few images identical to the "NO" photo, which quickly led to an earlier, unaltered version of the photograph:
The angle and pattern of lit windows in the tower and surrounding buildings are identical in both photos (except for the "NO" in the second photo):
While the "NO" is missing from the first photo, there's an identical pattern of lights on both Trump Tower Chicago and adjacent buildings. That suggests a political protest courtesy of Photoshop, not disgruntled residents of the building.