Based on the description of the map, Region A contains some red shading, which indicates a population density of 1,000 persons per square kilometer or more. This is the highest density range listed on the key. The other regions (B, C, and D) do not have red shading and only reach up to orange shading (250 to 999 persons per square kilometer) at their highest densities.
Therefore, Region A contains the highest population density.