We investigate the Néel temperature of Sr 2 CuO 3 as a function of the site dilution at the Cu ͑S =1/2͒ sites with Pd ͑S =0͒, utilizing the muon spin relaxation ͑SR͒ technique. The Néel temperature, which is T N = 5.4 K for the undoped system, becomes significantly reduced for less than one percent of doping Pd, giving a support for the previous proposal for the good one-dimensionality. The Pd concentration dependence of the Néel temperature is compared with a recent theoretical study [S. Eggert, I. Affleck, and M. D. P. Horton, Phys. Rev. Lett. 89, 47 202 (2002)] of weakly coupled one-dimensional antiferromagnetic chains of S =1/2 spins, and a quantitative agreement is found. The inhomogeneity of the ordered moment sizes is characterized by the SR time spectra. We propose a model that the ordered moment size recovers away from the dopant S = 0 sites with a recovery length of Ϸ 150− 200 sites. The origin of the finite recovery length for the gapless S =1/2 antiferromagnetic chain is compared to the estimate based on the effective staggered magnetic field from the neighboring chains.