Interplanetary dust particles (IDPs) collected in the Earth's stratosphere and meteorites are fragments of comets and asteroids. These are 'primitive' meteorites in part because they have preserved materials which predate the formation of the Solar System. The most primitive (least altered) meteorites contain a few parts per million of micrometre-sized dust which formed in the atmospheres of giant stars. Some meteorites have elevated D/H and 15N/14N ratios that are attributed to surviving interstellar organic molecules which have probably been strongly diluted and altered by parent-body processes. Most IDPs are chemically, mineralogically, and texturally primitive in comparison to meteorites. Here I show that H and N isotopic anomalies among fragile 'cluster' IDPs are far larger, more common, and less equilibrated than those previously observed in other IDPs or meteorites. In some cases, the D/H ratios that we measure reach the values of interstellar molecules, suggesting that molecular-cloud material has survived intact. These observations indicate that cluster IDPs are the most primitive class of Solar System materials currently available for laboratory analysis.