Bob and Elizabeth Rueland (David Duchovny and Joely Richardson) live and work in Chicago — Bob as an architect, Elizabeth as a zoologist at Lincoln Park Zoo.
On the night of her fundraiser for a new primate house, Bob promises Elizabeth he’ll finish the building. Elizabeth is killed in a car accident leaving the fundraiser, and her heart is transplanted to artist Grace Briggs (Minnie Driver), who has suffered from heart disease since the age of 14 and is near death.
The surgery is successful; Grace is able to live a normal life for the first time and plans to make her first airplane trip to Italy to paint. Grace’s best friend Megan Dayton (Bonnie Hunt), encourages her to start dating in spite of her self-consciousness about the long surgical scar on her chest.
Grace writes a letter to the donor’s family after the surgery, thanking them for the heart she received; it takes her over a year to finally find the courage to mail the letter. Bob works to build the primate house Elizabeth raised money for; he is still depressed a year after her death. He recognizes that he must resume his life as he becomes frustrated seeing that his dog hasn’t gotten over the loss either. His friend, veterinarian Charlie (David Alan Grier), organizes a blind date for him at O’Reilly’s, a self-styled Irish-Italian restaurant. The date goes very badly, but Bob finds that he is interested in the waitress — Grace, who is also the granddaughter of the restaurant’s owner, Marty O’Reilly (Carroll O’Connor).
Although they are both unaware of the connection they have through Elizabeth’s heart, Bob and Grace begin to date. As they grow closer together, Grace is reluctant to tell Bob about her medical history. After several months of dating, Grace finally decides to tell Bob about her transplant. However, before she gets the chance, she finds in his house the letter that she had sent several months earlier. Horrified by the discovery, Grace flees and tells Megan what has happened. Megan’s husband, Joe, (Jim Belushi) becomes infuriated as he has misunderstood Grace’s panic and thinks Bob must be married. Megan then explains the situation to him in six monosyllables: “Grace has Bob’s dead wife’s heart!” When Grace meets Bob again, she tells him the truth. Stunned and not knowing what to say, he leaves.
Against Megan’s advice to not run away from the situation, Grace goes to Italy alone. Back at home, Bob realizes that although he will always miss Elizabeth, he “aches” for Grace. He decides to go after her, and the two reunite in Italy. They return to Chicago for the dedication of the new primate house.
As the film ends we see Wally (William Bronder) and Sophie (Marianne Muellerleile) dancing happily at their wedding reception at O’Reilly’s restaurant, and Charlie holding Joe and a visibly pregnant Megan’s toddler, while they join Grace and Bob on the dance floor.