Double or Single Quote Marks for Quotes Inside Block Quotes?

[Lakai]

When there is a quote within a regular quote, single quote marks are used. I assume this is done to separate them from the double quote marks around the outside quote.

But what about a block quote that doesn't have the double quote marks around it. Should quotes inside a block quote use double or single quotes?

[BigT]

I believe you use double quotation marks. A quick look at the online Chicago Manual of Style confirms this:

Although material set off as a block quotation is not enclosed in quotation marks, quoted matter within the block quotation is enclosed in double quotation marks (CMS 11.35).

Note that this if from another source (http://www.globalautonomy.ca/global1/guidelines.jsp) that quotes it, since the online CMS is paywalled.