I don't know what server you are using. The only MOLAP server that I know of that will cope with this is TM1. Various ROLAP servers will cope with this.
I know MOLAP Servers best. One tip I would give you is to introduce more consolidation levels into the dimension, even if they are artificial splits like a consolidation of A-M and N-Z. Adding consolidations can improve performance as it lets the OLAP Engine section the data. If it has to go straight from 1 million elements to a single top level number then for whatever reason this is harder than adding up via several intermediate levels.
For OLAP Services I remember reading an article from the MSoft web site about very large dimensions. You'll have to search for it as I don't have it any more. My home ---->
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