The effects of cross‐diffusion on the onset of convective instability in a horizontally unbounded, triply diffusive, and triply stratified fluid layer (triply cross‐diffusive fluid layer) are investigated. Analytical solutions are obtained for steady and oscillatory onset when imposed gradients of the stratifying agencies are constant and vertical. Numerical results are based on diffusivity data for the system water/potassium chloride/potassium phosphate/phosphoric acid solution. Depending on the magnitude of the stratifying agencies, linear stability analysis shows that cross‐diffusion can either stabilize or destabilize a fluid layer. The off‐diagonal elements of the diffusivity matrix, which arise naturally as a result of the coupling among the various stratifying agencies, may strongly affect boundaries of convective stability and neutral curves. Discrepancies in the linear stability criteria were observed for seemingly negligible off‐diagonal elements of the diffusivity matrix.