  Using a highly efficient Monte Carlo algorithm, we are able to study the
growth of coverage in a random sequential adsorption (RSA) of self-avoiding
walk (SAW) chains for up to 10^{12} time steps on a square lattice. For the
first time, the true jamming coverage (theta_J) is found to decay with the
chain length (N) with a power-law theta_J propto N^{-0.1}. The growth of the
coverage to its jamming limit can be described by a power-law, theta(t) approx
theta_J -c/t^y with an effective exponent y which depends on the chain length,
i.e., y = 0.50 for N=4 to y = 0.07 for N=30 with y -> 0 in the asymptotic limit
N -> infinity.
