Love the lack of information here. As a Bostonian, let me clear this up.
The CEO of Chic-fil-a has made many statements over his career that he believe gay marriage is sinful and an affront to his god. He, using money from his business, donates money to groups that are known to discriminate against gay couples and are politically active in the denial of gay people their right to marry - I can't recall the name of the major one, but they run ads all the time on tv.
Now, Chic-fil-a wants to open up a franchise here in Boston in a particularly historic area (and we're an area that takes our historical areas and landmarks very, very seriously). In response to this, Mayor Menino (henceforth to be called Mumbles) said that they are not welcome here due to the discriminatory nature of their business. Gay marriage is legal here, Massachusetts being the first state to legalize it, and Menino says he does not want a company operating here that will actively discriminate and perpetuate hate against any citizens of the Commonwealth. He would later say that he would block any attempts made by Chic-fil-a to purchase the site and develop on it, and should it go through he would make it difficult for them to receive the required construction permits.
I don't disagree with Mumbles' main point - a company known for it's anti-gay stances will not be well received here. There's no questions about that. What he did that is wrong is suggest that he would use his position as Mayor of Boston to legal make difficult or prohibit Chic-fil-a from opening up shop in the city. That would be abuse of his authority, and quite frankly, grounds for his impeachment (though he wouldn't lose an impeachment vote...). Legally, Chic-fil-a has the right to open up shop here, just as the people of the Boston metropolitan area have the right to boycott; that's simply the free market. And, hell, if the people of Boston really do not want it at that particular site, they can write a petition to prevent the purchase from happening - numerous cities and towns have done similar to other companies for different reasons.
And, @GX7 , it has nothing to do with the CEO or the company being "Christian". I think you're forgetting that our Mayor is Christian, as well as the vast majority of the state. The problem Mumbles and the city have is the discriminatory nature of company and its owner.