Early Chicago Polish Newspapers Online
Newspaper death notices are very useful for establishing family relationships. A death notice index for the Dziennik Chicagoski is on this site. If your relative had a death notice published in that newspaper from 1890 through 1942, you can now see the death notice online. Just select the year and the date. Death notices are usually set off in black lined boxes. This service is provided by the Center for Research Libraries (CRL).
Update 9/19/2021: They used optical character recognition (OCR) to make the newspaper text searchable. I have not found a master OCR index that can be searched for the entire run of the newspaper or even for a complete day's issue. Instead, it seems that each page that can be displayed can be searched. Its accuracy depends on the quality of the printing-- clearer printing gives better OCR quality. Items appearing in Notatki Reportera can be hard to find since there's nothing to distinguish one item from another short of reading the whole column if what you are looking for occurs near the end. That's when I started using the search feature with some success. I was very cautious to put as little information in the search box as possible. The OCRed name may have defects that could cause the search to fail. For example, I might enter just Bar (or some other part of the name) instead of the whole name, Baranowski. I checked the 'Highlight all' box so that all instances matching the partial name stand out on the page. Even if there are a few matches, you can decide which (if any) are worthy of further attention. The search uses the Polish alphabet so Stanisław will not be found if you use Stanislaw. Be aware that word breaks can mess up a search so searching for Pryga might not turn up a result if the name was divided as Pry at the end of a line and ga beginning the next line. One last consideration is grammatic changes in a name where a nominative Szymańska might appear as Szymańskiej. So I might be inclined to search on just Stan instead of Stanisław or Stanislaw. In the second case I might just search on szym instead of Szymańska or Szymańskiej. While I focus on a surname during a search of the newspaper, I will switch to searching on a given name if I strike out on the surname.
The CRL also has a limited run of the Dziennik Związkowy primarily from 1908 to 1917 with a few more years as well. Access can begin here.
The same provider of these links also said the Dziennik Związkowy publisher sent their old issues to Poland for restoration and digitization. It may take another 3 years to complete but will be something to look forward to.