It's here.
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Ready for Skype? Here it is! Get it by accessing Network Update on your PSP. Here are the official details:
* Support for PLAYSTATION Network titles has been expanded.
* Skype has been added as a feature under Network.* (Only for PSP-2000 series.)
For more details on Skype and their free and paid calling services, visit the Skype official website. Note: Skype requires a PSP headset with remote control.
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It gives a compatible model list for Skype when you go to upgrade. The numbers are: PSP-2001, PSP-2002, psp-2003, PSP-2004, PSP-2005, PSP-2006, PSP-2007, PSP-2008, PSP-2010
Check your model numbers before you upgrade so you can see if you can use Skype or not.
Please note that if you upgrade to 3.90 you will lose all homebrew capabilities.