He graduated from Haverford College in 1941, having majored in Latin, was a naval officer during World War II, and after it spent a stint as interpreter at the War Crimes Investigation in Nuremberg and one year at the University of Zurich studying archaeology and classical philology before winning a Rome Prize Fellowship for the American Academy in Rome (1947-49).
In 1953 he married Elizabeth Chase, a graduate student of the American School of Classical Studies at Athens. Robert Hecht had three daughters: Daphne Howat by his first marriage to Anita Liebman; and Andrea and Donatella Hecht by his marriage to Ms. Chase. He lived for many years in Paris and died at home there.
Hecht made his first significant sales in the 1950s, including the dispersal of the collection of Ludwig Curtius, former director of the German Archaeological Institute in Rome, and later the sale of a late 6th century BCE red figure vase to the Metropolitan Museum of Art. In the 1960s and 1970s he reached a pre-eminent position in the trade. Known throughout the museum world for his scholarship and his 'eye' for antiquities, he sold to all the world's major museums including the British Museum, the Louvre, the Metropolitan, the Ny Carlsberg Glyptotek, the Museum of Fine Arts, Boston, and to many private collectors all over the world. Other dealers tended to give him first refusal on their 'finds'.
It was a period when major museums and serious collectors in Europe, the U.S., and Japan did not feel it their responsibility to enforce the export laws of southern European countries. Hecht always worked on the assumption that it was the preservation and study of ancient art that really mattered, not provenance. In the 1970s Bruce McNall was his "secret United States partner."
The sale of a Euphronios krater to the Metropolitan Museum of Art for $1 million in 1972 catapulted Hecht into instant fame and international problems. The Italians claimed that the vase was excavated illegally in Cerveteri, north of Rome. An American Grand Jury, investigating the Euphronios krater at the request of the Italians — whose evidence came from a tomb robber — found the provenance unproven. However, in 2006, continuing pressure from Italy led Philippe de Montebello, director of the Metropolitan Museum of Art, to negotiate a deal which gave the Italians ownership of the vase.
Hecht had wrangles with both the Italian and Turkish authorities but was acquitted in the only lawsuit to reach Italy's Supreme Court of Cassation (Suprema Corte di Cassazione).
In 2005 Hecht was indicted by the Italian government, together with Marion True, the former curator of antiquities at the J. Paul Getty Museum in Los Angeles, for conspiracy to traffic in illegal antiquities. The primary evidence in the case came from the 1995 raid of a Geneva, Switzerland warehouse which had contained a fortune in stolen artifacts.
Italian art dealer Giacomo Medici was eventually arrested in 1997; his operation was thought to be "one of the largest and most sophisticated antiquities networks in the world, responsible for illegally digging up and spiriting away thousands of top-drawer pieces and passing them on to the most elite end of the international art market". Medici was sentenced in 2004 by a Rome court to ten years in prison and a fine of 10 million euros, "the largest penalty ever meted out for antiquities crime in Italy".
The court hearings of the case against Hecht and True ended in 2012 and 2010, respectively, as the statute of limitations, under Italian law, for their alleged crimes had expired.