I assume that there is sufficient base and chlorine and that the conditions are vigorous enough to get beyond dichloride 4, which, being a non-enolic β-diketone at C3, is labile toward Haller-Bauer-type cleavage. Acetylacetone 1 is highly enolic and readily deprotonated. The first two chlorinations lead to dichloride 4. Cleavage of dichloride 4 with base gives enolate 6 which can be protonated by water, or to save space, chlorinated to provide the trichloroketone 8, which is an intermediate in the haloform reaction of acetone. Cleavage with base leads to chloroform (10) and a second equivalent of sodium acetate (7).