In "the not-too-distant future", eugenics is common. A genetic registry database uses biometrics to classify those so created as "valids" while those conceived by traditional means and more susceptible to genetic disorders are known as "in-valids". Genetic discrimination is illegal, but in practice genotype profiling is used to identify valids to qualify for professional employment while in-valids are relegated to menial jobs.
Vincent Freeman is conceived without the aid of genetic selection; his genetics indicate a high probability of several disorders and an estimated life span of 30.2 years. His parents, regretting their decision, use genetic selection to give birth to their next child, Anton. Growing up, the two brothers often play a game of "chicken" by swimming out to sea with the first one returning to shore considered the loser; Vincent always loses. Vincent dreams of a career in space travel but is reminded of his genetic inferiority. One day Vincent challenges Anton to a game of chicken and bests him before Anton starts to drown. Vincent saves Anton and then leaves home.
Vincent works as an in-valid, cleaning office spaces including that of Gattaca Aerospace Corporation, a space-flight conglomerate. He gets a chance to pose as a valid by using hair, skin, blood and urine samples from a donor, Jerome Eugene Morrow, who is a former swimming star paralyzed due to a car accident. With Jerome's genetic makeup, Vincent gains employment at Gattaca, and is assigned to be navigator for an upcoming trip to Saturn's moon Titan. To keep his identity hidden, Vincent must meticulously groom and scrub down daily to remove his own genetic material, and pass daily DNA scanning and urine tests using Jerome's samples.
Gattaca becomes embroiled in controversy when one of its administrators is murdered a week before the flight. The police find a fallen eyelash of Vincent's at the scene. An investigation is launched to find the murderer, Vincent being the top suspect. Through this, Vincent becomes close to a co-worker, Irene Cassini, and falls in love with her. Though a valid, Irene has a higher risk of heart failure that will prevent her from joining any deep space Gattaca mission. Vincent also learns that Jerome's paralysis is by his own hand; after coming in second place in a swim meet, Jerome threw himself in front of a car. Jerome maintains that he was designed to be the best, yet wasn't, and that is the source of his suffering.
Vincent repeatedly evades scrutiny from the investigation, and it is revealed that Gattaca's mission director was the killer, as the administrator was threatening to cancel the mission. Vincent learns the identity of the detective who closed the case, his brother Anton, who has become aware of Vincent's presence. The brothers meet, and Anton warns Vincent that what he is doing is illegal, but Vincent asserts that he has gotten to this position on his own merits. Anton challenges Vincent to one more game of chicken. As the two swim out in the dead of night, Anton is surprised at Vincent's stamina, and Vincent reveals that his trick to winning was not saving energy for the swim back. Anton turns back and begins to drown, but Vincent rescues him and swims them both back to shore using celestial navigation.
On the day of the launch, Jerome reveals that he has stored enough DNA samples for Vincent to last two lifetimes upon his return, and gives him an envelope to open once in flight. After saying goodbye to Irene, Vincent prepares to board but discovers there is a final genetic test, and he currently lacks any of Jerome's samples. He is surprised when Dr. Lamar, the person in charge of background checks, reveals that he knows Vincent has been posing as a valid. Lamar admits that his son looks up to Vincent and wonders whether his son, genetically selected but "not all that they promised", could break the limits just as Vincent has. He passes Vincent as a valid. As the rocket launches, Jerome dons his swimming medal and immolates himself in his home's incinerator; Vincent opens the note from Jerome to find only a lock of Jerome's hair attached to it. Vincent muses on this, stating "For someone who was never meant for this world, I must confess, Iâm suddenly having a hard time leaving it. Of course, they say every atom in our bodies was once a part of a star. Maybe I'm not leaving; maybe I'm going home."

Question: Why can't Irene go on any space missions? 
Answer: She has a high risk of heart failure.
Alternative answer: higher risk of heart failure disqualifies her