Properties of biological fitness landscapes are of interest to a wide sector of the life sciences, from ecology to genetics to synthetic biology. For biomolecular fitness landscapes, the information we currently possess comes primarily from two sources: sparse samples obtained from directed evolution experiments; and more fine-grained but less authentic information from 'in silico' models (such as NK-landscapes). Here we present the entire protein-binding profile of all variants of a nucleic acid oligomer 10 bases in length, which we have obtained experimentally by a series of highly parallel on-chip assays. The resulting complete landscape of sequence-binding pairs, comprising more than one million binding measurements in duplicate, has been analysed statistically using a number of metrics commonly applied to synthetic landscapes. These metrics show that the landscape is rugged, with many local optima, and that this arises from a combination of experimental variation and the natural structural properties of the oligonucleotides.