A single monolayer of iron selenide grown on strontium titanate shows an impressive enhancement of superconductivity compared with the bulk, as well as a novel Fermi surface topology, extreme two-dimensionality, and the possibility of phonon-enhanced electron pairing. For films thicker than one unit cell, however, the electronic structure is markedly different, with a drastically suppressed superconductivity and strong nematicity appearing. The physics driving this extraordinary dichotomy of superconducting behaviour is far from clear. Here, we use low-temperature scanning tunnelling microscopy to study multilayers of iron selenide grown by molecular beam epitaxy, and find a stripe-type charge ordering instability that develops beneath the nematic state. The charge ordering is visible and pinned in the vicinity of impurities. And as it emerges in the strong limit of nematicity, it suggests that a magnetic fluctuation with a rather small wavevector may be competing with the ordinary collinear antiferromagnetic ordering in multilayer films. The existence of stripes in iron-based superconductors, which resemble the stripe order in cuprates, not only suggests that electronic anisotropy and correlation are playing an important role, but also provides a platform for probing the complex interactions between nematicity, charge ordering, magnetism and superconductivity in high-temperature superconductors.