The chain ladder forecast of oustanding losses is known to be unbiased under suitable assumptions. According to these assumptions, claim payments in any cell of a payment triangle are dependent on those from preceding development years of the same accident year. If all cells are assumed stochastically independent, the forecast is no longer unbiased. Section 6 shows that, under very general assumptions, it is biased upward. This result is linked to earlier work on some stochastic versions of the chain ladder.