Sorting groups of rows by a cell in that group

Hello,
I am looking for a way of doing something which is beyond my ability and I hope you can help please. I will explain the overall task and where I have managed to get to.

I first want to group rows of data by one field within that row (I've got that far). Here is where I fall over so to speak....
I then want to sort those groups by one of the fields in that group.
To put it into context, I have rows of data which have a customer identification number and also a date field. There will be rows with the same customer number but different dates. I would like to group the rows by the customer number, but then sort the groups into chronological order of when that customer first appears in the spreadsheet.

I have included an example, column A is the customer identifier and column B is the date (there is also time in that field but I have found that the =MIN() function still finds the earliest date and time).
I'm sorry there is a lot of data but this way I can definately say that there are duplicate customers with different dates.
So to summarise, I would like the rows grouped by column A, and then those groups to be sorted by the earliest date that is in that group.

I hope that makes sense.

Many thanks in advance.