We consider a three-terminal state-dependent relay channel with the channel state available non-causally at only the source. Such a model may be of interest for node cooperation in the framework of cognition, i.e., collaborative signal transmission involving cognitive and non-cognitive radios. We study the capacity of this communication model. One principal problem in this setup is caused by the relay's not knowing the channel state. In the discrete memoryless (DM) case, we establish lower bounds on channel capacity. For the Gaussian case, we derive lower and upper bounds on the channel capacity. The upper bound is strictly better than the cut-set upper bound. We show that one of the developed lower bounds comes close to the upper bound, asymptotically, for certain ranges of rates.