The mean first passage time for the close approach of the ends of a polymer is investigated by computer simulation of the Brownian dynamics of a Rouse model. There are N bonds, of length b, and the contact distance is a. The results for N=50, 75, and 100 are compared with theoretical predictions by Wilemski and Fixman (WF), and by Szabo, Schulten, and Schulten (SSS). Theory differs from simulation by a factor of 1.3 to 3 when a is comparable to b but improves considerably when a is reduced. Closest agreement is obtained at a/b = 0.1 for WF with a delta function sink, where theory is within the statistical error (approximate to 5%) of the simulation for each case.