I'm not sure there is a "chief" irony in Chopin's "The Story of an Hour." Does there have to be a "major" irony as opposed to "minor" ironies? You can take your pick among many. It is ironic that the news of the death of her husband is supposed to make her sad but instead makes her rejoice. It is ironic that in a patriarchal society often the only chance a woman has to succeed is to improve her social/economic standing by marrying wealthy, but she feels a tremendous sense of freedom when she hears that her husband is dead. It is ironic that the news that her husband is actually alive is supposed to make her rejoice but instead makes her drop dead. If there is an underlying or "major" irony, it might be the reversal of roles: it is not the male who is trapped here, it is the female. She is so elated at the glimpse of freedom she experiences that the revelation that she is not free is too much to bear.
Irony can be found all throughout the story, indeed. For example, it is ironic that Brently Mallard, who we had been told was dead, was indeed alive and walked in at the end. It is ironic that at the end, Louise dies of a heart attack, when all through the story itself, it was her husband who we thought had died, AND that she died upon good news and not bad like they were worried about.
However, given the main theme that comes out in many of Kate Chopin's stories of women who are discontented in their alloted roles as houswives, the main irony would have to relate to the fact that Louise, upon the news of her husband's death, was not sad. Sure, she wept, and, as the story states, "she would be sad" when she saw him at the funeral, but, her main reaction is overwhelming and exilerating joy. That is not a typical reaction to the news of the death of a loved one--it is ironic in a way that supports Chopin's main point. Her message conveyed the idea that sometimes, women of her time period were not happy in marriage, even if that marriage was good. She wrote many stories that had women finding happiness outside the bounds of marriage itself. Louise Mallard's reaction is quite extreme; she sits in her chair and is filled with elation at the possibility of freedom from being married. She is overwhelmed with happiness, and that is the main irony that exists in this story, the one that comes through the most strongly. I hope that helped; good luck!