Only if:
- you control the first proxy, and can configure it to route requests to the second proxy
- or the first proxy accepts some special syntax to control routing the requests (eg, it could convert
http://realsite.com.proxy2.example.com/ into a request to http://realsite.com/ routed via proxy2.example.com. I'm not aware of anything that does this out of the box.
TOR (wikipedia) does something similar to what you're after. Every packet that goes over TOR goes through ~3 intermediate hops. only the first intermediate hop knows where the traffic came from (but can't tell what was in the traffic; nor its ultimate destination). Only the last intermediate hop knows where the traffic is going (and what the unencrypted data is) - but it doesn't know where the data came from, nor does it know how to contact a machine that knows where the data came from.
This isn't perfect, but it's a good start towards anonymity.