B chromosomes are genome symbionts, the presence of which in many eukaryote species is explained, in most cases, by their violation of Mendelian rules, usually based on meiotic or mitotic instability, leading to their accumulation in the germ line (drive). However, B chromosome integration into the genome as a regular member of the chromosome set should imply the loss of drive. A possible way of bypassing this difficulty is to regularize meiosis when the B chromosome is frequent in the population, in order to yield gametes with one B chromosome. In diploid organisms, this task needs to be achieved in the two sexes, but in haplodiploids the problem simplifies to only the diploid sex. We have found, to the authors' knowledge, the first evidence of a B chromosome that is regularizing its meiotic behaviour and limiting its number to one B chromosome per haploid genome, the same dosage as the standard (A) chromosomes, in the solitary wasp Trypoxylon albitarse. It suggests a possible mechanism for B chromosome integration as a regular member of the chromosome complement.