In this paper, a search is made to detect any sort of nonlinearity and chaos in the solar irradiance data from the Earth Radiation Budget Satellite during the time period from October 15, 1984 to October 15, 2003 in order to investigate the inherent complexity in it. In this paper, delay vector variance analysis has been applied to trace the nonlinearity; whereas 0-1 test, correlation dimension analysis, information entropy, recurrence plot, and recurrence quantification analysis have been used to explore the signature of chaos in the present time series. Present investigation reveals that though nonlinearity is significantly present in the signal, chaotic behavior is not really observed in it.