Mo. Rev. Stat. § 64.140
The regulations imposed and the districts created under authority of sections 64.010 to 64.160 may be amended from time to time by the county commission by order after the order establishing the same has gone into effect, but no such amendment shall be made without a hearing before the county planning commission; or if there be no county planning commission, such hearing shall be held by the county zoning commission. Such hearing shall be held in any one place in the county designated by the planning or zoning commission regardless of the location of the land affected by such amendment or amendments. Public notice of such hearing shall be given by at least one publication in one newspaper published in the county at least fifteen days before the date of the hearing. In case of written protest against any proposed amendment, signed and acknowledged by the owners of thirty percent of the frontage within one thousand feet to the right or left of the frontage proposed to be changed, or by the owners of thirty percent of the frontage directly opposite, or directly in the rear of the frontage proposed to be altered, or in cases where the land affected lies within one and one-half miles of the limits of a municipality, by the city council or zoning board of any such municipality, filed with the county clerk, such amendment may not be passed except by the favorable vote of two-thirds of all the members of the county commission.
§ 64.140, RSMo