Recent developments in the theory of non-linear dynamical systems have been used to find dimensionality of the chaotic behaviour of the short term fluctuations in the Length of Day (LOD). Here we report, for the first time, the measure of attractor dimensions in the latest LOD data spanning over a period of approximately 15 years (1976--1990). Our analysis of daily variations of LOD indicate an evidence of low dimensional attractor of the system in the range 5 to 7. It can be inferred that the underlying dynamics has limited degrees of freedom and influenced by non-random atmospheric and oceanic processes. We believe that the results may help to constrain models of linkages between earth's rotation and air-sea interactions. ¿ American Geophysical Union 1992