Laboratory tests have been undertaken on a relatively undisturbed sample of a mudline clay that was retrieved from within a giant scour from c. 4600 m below sea-level in the Atlantic Ocean to the west of the Iberian Peninsula. The geotechnical tests reported here shed light on the regional geological history and scour formation, which can be of economic importance as infill material inside fossil scours is often a hydrocarbon exploration target. Test data indicate that the scour-infill material from this site has not been exposed to sufficient vertical effective stress for it to develop any appreciable stress-induced structure. Furthermore, they confirm the hypothesis that the scour-infill sediment tested post-dates scour formation. An oxidation front is also observed in the sample, which is common in submarine sediments. Tests either side of the oxidation front have shown that the differential weathering across it changes the liquidity index of the material but does not significantly change the compressibility characteristics. The sediments tested, whose behaviour has been interpreted using sensitivity and intrinsic strength frameworks, are recently deposited, and are therefore at the initial stage of their geological life. Thus, the soil parameters derived can provide useful reference values against which other sediments, which may have undergone some diagenesis and compression, can be compared. It should be noted that the present study is unique as it has focused on high-quality samples of these highly compressible deep-sea sediments, retrieved from within the top layers of the sedimentary strata, in contrast to other studies that are normally completed on samples taken from several metres depth below the seabed and/or show more disturbance.