My partner has HSV-1. Can he give me genital herpes by performing oral sex?

Yes, I'm sorry to say he could. HSV-1 and 2 are almost indestinguishable. The distinctive features tend to be where the virus lives during its 'dormant' stage (latency).

HSV-1 locates itself in nerves near the ear and when it becomes active the results are seen around the mouth and lips. Conversely, HSV-2 is often associated as the genital herpes virus because it is located in nerves around the base of the spine. When it becomes active the outbreaks are seen in and around the genitals.

There is however the potential for cross-over and in some countries genital herpes with HSV-1 is as common as HSV-2. Charlotte Grayson M.D. has written a useful Sharepost on this very topic called Genital Herpes - the truth about HSV1, HSV2 and Oral Sex that you might like to read.