In short, Mary Anne and Robert De Grimston met in London through the Church of Scientology, which they split from rather quickly. In 1965/66 the Process began in earnest, having chapters in many cities around the world. They attracted a good deal of controversy for their belief system, which involved a "worldview that accepted Lucifer, Jehovah, Satan and Christ as partners in a larger godhead." (Quote courtesy the Gnostic Liberation Front, whose information regarding the Process is quite extensive) Some referred to them as Satanic, some as a cult. It was alleged at one point that Charles Manson was a member, though this was found to be untrue.
This image from the "Death" issue of the Process magazine, blatantly stolen from Gnostic Liberation Front.
I've found three locations in Chicago which somehow related to the Process in the 1970s. According to Feral House, the Chicago Chapter was founded in 1970. As a testament to the prevalence of Processians in Chicago during this time period, I happened upon an article in a friend's zine collection which described how the black-caped Processians would be seen around town, spreading the word (if I can track this article down again, I'll post it here). Another mention of both their capes and their magazines made its way into the Chicago Tribune, August 11 1974.
After this, the exact timeline of Chicago residences gets a bit hazy.
Feral House states that the Chicago chapter was founded on Wells Street. I have an address for the Foundation Church of the Millenium (a later variant of the Process after a schism erupted when Mary Anne and Robert DeGrimston separated) in 1976 at 1529 N Wells St. This location is now home to a Subway sandwich shop.
At some point the local chapter of the Process was located a mile away from the Wells location, on Burling Street. This is a 1892 square foot home built in 1869. This area of town is very affluent now, though I've seen some mention of it being "slums" at one point. There is a mansion across the way, but I found that it wasn't built until 2001.
A quick Internet search finds a poster going by the name of "stubby" on a Chuck Palahniuk message board who says that he was a member of the Process for three years in Chicago. He says that the chapter house was on Deming and the Process's coffee house was in Old Town, which I assume to be the Wells location. The fact that the Process was potentially operating out of two locations simultaneously in the city says something about their size.
I'm posting another article about the Process below, though it is only related by a single woman who murdered a man. The woman in question appears to have joined (or claimed to have joined) every occult organization possible in Chicago, and the local community speaks out. Chicago Tribune, February 4th 1981.