Monte Carlo simulations utilizing the bond fluctuation method for a square lattice were performed to simulate the dynamics of two-dimensional polymer chains. Relaxation times of the modes were determined as were average intrachain distances. Scaling exponents were found relating the relaxation times with mode number and the total number of chain segments. Scaling exponents relating intrachain distance with mode number and the total number of chain segments were also found. Scaling behavior indicated that internal fragments of the chains were more expanded than would be the case of a self-similar chain but that the higher order modes relaxed more quickly relative to the lower order modes than would be the case for a Rouse chain. Small but noticeable cross-correlations between the modes were observed.