New Chain causing skipping on cassette - will this work itself out or is it unsafe?
Over time an old chain and cassette wear together, so you don't notice the wear until it gets really bad.  When you replace the chain while leaving the old cassette the tooth profile is no longer correct and the new chain will skip off of the teeth, especially under load. 

Unfortunately it won't get better and the only recourse is to replace the cassette as well.  In the future you can save money by changing the relatively inexpensive chain more often as the cassette wears faster with an elongated chain.

More info:  http://sheldonbrown.com/chains.html