Yes, the chalkhill blue is only found on chalk hills; well, include limestone hills as well as they are both calcareous in their formation. I confess that although I try not to have 'favourites' the chalkhill blue to me is a most beautiful insect and I never tire of seeing them but sadly they have declined, like many other species, due to habitat loss. Much chalk grassland was ploughed for crops during the second world war and then the coming of myxomatosis in the rabbit population in the 1950s saw less grazing of grasses to provide the short sward this butterfly needs. Nevertheless there are a number of populations throughout Dorset although some are small and struggling to survive. They need horseshoe vetch for their larvae to feed on and this is quite widespread in the county so given that the right conservation measures are in place hopefully the chalkhill blue is safe.
The chalkhill blue has a single brood each summer and they can be seen from mid-July through until early September. We only have thirteen reports for 2017 and 2018 in the Nature of Dorset database which is not much to work on but there are reports from week 27, on schedule in the middle of July, and then almost continuously until week 38 in early September; textbook stuff!
If you know a bit about the geology of Dorset then the distribution map will mean something to you as the bulk of sites where the chalkhill blue can be found lie along the chalk ridge from around Maiden Newton to Shaftesbury. There is a strong population on Portland, especially in Tout Quarry where many of the reports come from. They can also be found on the Purbeck coast around Lulworth, especially on Bindon Hill.