The article about Revd Paul Morgans, previously from St Peter's church in Pentre, south Wales, was written by the Telegraph in 1999.
It's been taken down as part of a European law which means "inadequate, irrelevant or no longer relevant" can't be linked to through search engines.
For the website to have been removed an official request must have been made to Google although the company will not say who made it.
The search engine does, however, require proof that the article relates specifically to the complainant or someone acting on his/her behalf.
At the time Revd Morgans had to be forced to leave the Vicarage by the Church of Wales after he resigned.
He then pinned a letter on the church door calling parishioners "exclusive and judging, trivial and insensitive".
He added that they had left him "burnt-out, damaged and heavily dependent on medication".
The EU law has been responsible for more than a quarter of a million requests for Google to take information down.