Y.-G. Chen conjectured that for any positive integer r, there are infinitely many sets of r consecutive integers that are all Sierpiński and Riesel, and he demonstrated this result for r = 5. In this paper, we prove a variation of Chen's conjecture. In particular, we show that for any positive integer r, there exists an arithmetic progression of positive integers k such that the set {k + 2t — 1 : 0 ≤ t ≤ r — 1} contains r Sierpiński integers.