Observations at Jodrell Bank are reported of very fine modulations of the dynamic spectra of interstellar scintillation (ISS) from pulsar PSR B0834+06. These fringes have a period in radio frequency of 45kHz, which is about 100 times smaller than the largest bandwidth due to normal ISS of the pulsar at the central observing frequency of 408MHz. Analysis shows good consistency with a model in which two ray-bundles intersect and interfere creating the fringes, from which a 22-mus delay difference is inferred. The separation between the bundles is greater than 4 mas which is more than 10 times their angular diameter. Such a large ratio cannot be due to an inner scale that cuts off the pervasive turbulent density spectrum responsible for the diffractive angular broadening. The fringing was observed on four occasions over 30d and so is similar to the `extreme scattering events' observed in other sources. 3 au is the scale inferred, and various possible structures in the interstellar plasma density are considered. A stochastic refraction model is proposed, in which many isolated regions in a layer of parsec thickness randomly build up enhanced angles of refraction. Normally neighbouring ray-paths do not intersect. However, occasionally their angles are large enough to cause interference and the associated fringes. A specific model is proposed in which the ionized refracting layer surrounds a warm Hi cloud, with anisotropic density irregularities of 0.25 electron cm^-3, which could be in equilibrium with the normal interstellar pressure.