Chondrules are igneous spherical objects preserved in chondritic meteorites and believed to have formed during transient heating events in the solar protoplanetary disk. Chondrules present in the metal-rich CB chondrites show unusual chemical and petrologic features not observed in other chondrite groups, implying a markedly distinct formation mechanism. Here, we report high-precision Mg-isotope data for 10 skeletal olivine chondrules from the Hammadah al Hamra 237 (HH237) chondrite to probe the formation history of CB chondrules. The Al/Mg ratios of individual chondrules are positively correlated to their stable Mg-isotope composition (μMg), indicating that the correlated variability was imparted by a volatility-controlled process (evaporation/condensation). The mass-independent Mg composition (μMg*) of chondrules is consistent with single stage formation from an initially homogeneous magnesium reservoir if the observed μMg variability was generated by non-ideal Rayleigh-type evaporative fractionation characterized by a β value of 0.5142, in agreement with experimental work. The magnitude of the mass-dependent fractionation (∼300 ppm) is significantly lower than that suggested by the increase in Al/Mg values, indicating substantial suppression of isotopic fractionation during evaporative loss of Mg, possibly due to evaporation at high Mg partial pressure. Thus, the Mg-isotope data of skeletal chondrules from HH237 are consistent with their origin as melts produced in the impact-generated plume of colliding planetesimals. The inferred μMg* value of -3.87 ± 0.93 ppm for the CB parent body is significantly lower than the bulk solar system value of 4.5 ± 1.1 ppm inferred from CI chondrites, suggesting that CB chondrites accreted material comprising an early formed Al-free component.