Singlet exciton fission is an exciton multiplication process that occurs in certain organic materials, converting the energy of single highly-energetic photons into pairs of triplet excitons. This could be used to boost the conversion efficiency of crystalline silicon solar cells by creating photocurrent from energy that is usually lost to thermalisation. An appealing method of implementing singlet fission with crystalline silicon is to incorporate singlet fission media directly into a crystalline silicon device. To this end, we developed a solar cell that pairs the electron-selective contact of a high-efficiency silicon heterojunction cell with an organic singlet fission material, tetracene, and a PEDOT:PSS hole extraction layer. Tetracene and n-type crystalline silicon meet in a direct organic-inorganic heterojunction. In this concept the tetracene layer selectively absorbs blue-green light, generating triplet pairs that can dissociate or resonantly transfer at the organo-silicon interface, while lower-energy light is transmitted to the silicon absorber. UV photoemission measurements of the organic-inorganic interface showed an energy level alignment conducive to selective hole extraction from silicon by the organic layer. This was borne out by current-voltage measurements of devices subsequently produced. In these devices, the silicon substrate remained well-passivated beneath the tetracene thin film. Light absorption in the tetracene layer created a net reduction in current for the solar cell, but optical modelling of the external quantum efficiency spectrum suggested a small photocurrent contribution from the layer. This is a promising first result for the direct heterojunction approach to singlet fission on crystalline silicon.