I'm a big believer in chains of migration, but while working on my wife's Frame family I completely ignored it. My theory was that since the 1869 era immigrant went to Chicago and was a painter that he simply settled there because he thought he could find work.
When searching for all his family's US census entries, I noted that one child was born in Pennsylvania. When searching UK census records on his in-laws, I noted that his wife had nephews in the UK who indicated they were born in Pennsylvania. Hmmm.
Maybe there was a chain of migration after all and I need to remind myself to look at the in-laws too!