Born at Bolton in Lancashire, Kroto was educated at the University of Sheffield where he completed his PhD in 1964. After a postdoctoral fellowship with the National Research Council of Canada, and two years with Bell Laboratories, New Jersey, Kroto moved to the University of Sussex (1967) where he was appointed professor of chemistry in 1985.

Along with his Sussex colleague David Walton, Kroto had a long-standing interest in molecules containing carbon chains linked by alternate triple and single bonds. Such chains with five, seven, and nine carbon atoms had been identified by radioastronomers in space. In 1984 Kroto heard that the American chemist Richard Smalley had developed new techniques involving laser bombardment for the production of clusters of atoms. He suspected they might be suitable to produce the chains of carbon atoms which interested him. Consequently in 1985 he visited Smalley in Houston.

Kroto persuaded Smalley to direct his laser beam at a graphite target. Clusters of carbon atoms were indeed produced but, more interesting than the small chains he was looking for, Kroto found a mass-spectrum signal for a molecule of exactly 60 carbon atoms. The first suggestion was that it had a sandwichlike graphite structure. However, such a planar fragment would have reactive carbon atoms at the edges, whereas C_{6 0} appeared to be stable. An alternative structure with the necessary lack of reactivity would be a spherical one in which the 60 carbon atoms are positioned at the vertices of a polyhedron. In Kroto and Smalley's model, which was later shown to be correct, the faces of the polyhedron are pentagons or hexagons arranged like the panels on a modern soccer ball. The framework also resembles the structure of the geodesic dome designed by the architect Buckminster Fuller. Kroto called C_{6 0} buckminsterfullerene, a name subsequently shortened to fullerene. Carbon molecules with this type of structure are informally called ‘bucky balls’.

Before the structure could be put beyond doubt sufficient C_{6 0} would have to be prepared for detailed spectroscopic analysis. This, however, proved unexpectedly difficult. On his return to Sussex Kroto began to work on the problem. Unfortunately funding was unavailable, even for relatively cheap experiments with graphite electrodes. It was consequently left to Kratschmer and Huffman to announce in 1990 that they had synthesized a new form of carbon. When he read a full description of the synthesis Kroto learned that he had been pursuing the same method two years earlier when he had been forced to abandon the project through lack of funds. For his contribution to the discovery of C_{6 0} Kroto shared the 1996 Nobel Prize for chemistry with Richard Smalley and Robert Curl.