The capacity of a state-dependent channel with rate-limited decoder state-information is the highest rate at which data can be transmitted reliably over the channel when the decoder-in addition to observing the channel output-is also furnished with a rate-limited state-description that is provided by a state-encoder observing the state-sequence noncausally. A lower bound on this capacity is derived here for the Gaussian state-dependent channel, with the lower bound being tight in the absence of noise. In this regime every additional bit of state-description increases capacity by one bit. At the other extreme, when the signal power is much smaller than the noise and state powers, capacity behaves asymptotically as though the state were known to the decoder precisely.