In Fallout: New Vegas, can I still get the Platinum Chip even with a vilified Legion reputation?

I'm vilified against Ceaser's Legion and have come to the part where I must obtain the Platinum Chip at the Fort. I want to do this part without killing anyone, especially Caesar. When I get there, I dress up as a Legionary and I manage to lose suspicion from everyone else, but when I get near a Legion dog, then everyone goes hostile towards me. Is there any way that I can still get the Chip without killing anyone?