Hi
I don't have any 3850 right now to test but private vlan should be supported on latest 3.7 version.
Base on this release notes, you can validate the private vlan supported:
http://www.cisco.com/c/en/us/td/docs/switches/lan/catalyst3850/software/release/3e/release_notes/rn-3dot7e-3850.html
Private VLAN support is introduced.
To download this latest version, go on Cisco website: https://software.cisco.com/download/release.html?mdfid=284455426&softwareid=282046477&release=3.7.4E&relind=AVAILABLE&rellifecycle=MD&reltype=latest
You need to go on All Releases menu then under 3 you will see 3.7 code.
Hope this helps.
Thanks
PS: Please don't forget to rate and mark as correct answer if this answered your question
Thanks
Francesco
PS: Please don't forget to rate and select as validated answer if this answered your question