Emotions in India are still raw, for the Bhopal disaster killed 15,000 people and injured half a million, according to the government, and is being blamed for major local health problems 27 years later.
Although Indian officials say the country has no intention of staying away from the games, pressure has been building for the Olympics to sever its ties with Dow or face the risk of constant protests marring the spectacle that Britain hoped would lift its flagging spirits and foundering economy.
Dow is one of the elite club of sponsors that the International Olympic Committee places in its "Top" category, enjoying a special status in exchange for paying about $100 million every four years.
Coe would have real trouble pulling out the rug from a sponsor with such status, particularly because the feel-good Olympic image is a main reason why Dow would sponsor the games in the first place. Companies pay big money to attach their brand to the warm and fuzzy glow of young, strong and photogenic athletes overcoming the odds to win on a world stage.
Much of the controversy stems from Dow's funding of the "wrap," an innovative curtain designed to encircle the stadium. Olympic officials scrapped the plan last year because its cost - 7 million pounds ($11.4 million) - seemed out of step with austere times across Europe.
Architects and artists decried the decision, suggesting the image of the games would suffer - never mind that fans trying to find their seats in the steel-latticed stadium would need something to guide them through the identical girders.
Then Dow swooped in to save the wrap - and didn't even blink at Olympic guidelines that will bar it from etching its brand logo onto the curtains.
Olympic organizers could face unpleasant consequences for being associated with a company linked to such an uncomfortable subject such as Bhopal.
"You run the risk of the association and sponsorship backfiring, to the extent that the Olympic Games might feel impacted by the relationship with Dow," said Scott Rosner, associate director of the Wharton Sports Business Initiative.
In India, where the Bhopal tragedy remains an open wound, survivors and their advocates said the Olympic wrap project with Dow ignores the immense pain they have suffered since gas and chemicals leaked out of the Union Carbide pesticide plant on Dec. 3, 1984.
Besides the massive number of dead and injured, residents say the area is still contaminated and the leak is causing birth defects and terrible health problems for those who remain.
Dow says that it had nothing to do with the leak. It only bought Union Carbide in 2001 - more than 16 years after the disaster. It said legal claims were resolved when Union Carbide reached a settlement with the Indian government and paid $470 million as compensation for those killed or injured.
Dow has expressed sadness about the disaster, saying that the "tragic events of 1984 have cast a long shadow over the people of Bhopal and the chemicals industry."
"Dow has never had any involvement with the Bhopal plant site or with the 1984 Bhopal gas release and efforts by certain interest groups to attach this to the company are misdirected and inappropriate," spokesman Scot Wheeler of Dow said in an email Friday.
The Michigan company's vocal critics say that is not enough. They argue the victims of the leak never got proper compensation, and have demanded that Dow make amends. The Indian government is seeking an additional $1.7 billion from Dow in compensation for the victims and their families.
Indian Olympic athletes and Bhopal victims' groups have urged the London organizers to boot Dow out, saying its continued involvement with the wrap endorses a company that is refusing to clean up the contaminated soil and groundwater in Bhopal. Dow and Union Carbide say the site is now owned by the state of Madhya Pradesh and the state is responsible for the cleanup.
Amnesty International has also condemned the Dow wrap deal, and several British politicians have campaigned to dump Dow from the games.
"What has given real offense to the people of Bhopal is that on this, the most sustainable games ever and lauded as such, that we should wrap the stadium, the big symbol of the games, in a skin that might as well be the skin of the families that died," said London lawmaker Barry Gardiner.
All of this comes just as Coe, a former gold-medal runner, should be taking a victory lap, with all the Olympic venues completed on schedule and no major scandals ahead of the July 27 to Aug. 12 event.
Instead, his likeness was burned and beaten by hundreds of protesters in the streets of Bhopal on Friday, on the eve of the 27th anniversary of the disaster. The protesters carried banners reading, "Down with London Dowlympics" and "We want justice" - and they planned to stop trains passing through the city Saturday as well.
Coe is being dogged at every public appearance now by questions on the Dow controversy.
His own personal history even comes into play: Coe is the grandson of an Indian. During a recent appearance before the U.K. Parliament's media, culture and sport committee, he tried, as he has repeatedly, to say that all the rules were followed.
"I am satisfied that the ownership, operation and the involvement either at the time of the disaster or at the final settlement was not the responsibility of Dow," he said.
Now his Olympic committee is facing a threat that would horrify any event manager. If it doesn't cut ties with Dow, protesters have vowed to hold their own "Bhopal Olympics" during the London games - an event contested by children with congenital disabilities attributed to the Bhopal gas leak.