Step 1: Trace where MIF comes from - it is anti-Mullerian hormone made by testicular Sertoli cells to regress the female ductal system in a male embryo. Step 2: A testis only forms when the $SRY$ gene, the testis-determining factor on the short arm of the $Y$ chromosome, switches on. Step 3: AMH production sits downstream of this SRY-driven testis formation, so the controlling chromosome is the Y chromosome. Step 4: Even though the AMH structural gene and receptor are autosomal, the question targets the chromosome responsible for triggering MIF production, which is the Y chromosome.\[\boxed{\text{Y chromosome}}\]