Khloe Kardashian -- I'm Here To Meet My New Nephew ... Arrives At Hospital

Khloe Kardashian is already earning points toward being Kim and Kanye's new baby's favorite aunt ... she's the first we've seen arrive at the hospital.

Khloe just pulled up to Cedars in Beverly Hills in her white Bentley ... still no sign of Kylie, Kourtney or Kendall but there's a good chance Kris was there for the birth.

As TMZ reported -- Kim and Kanye welcomed a baby boy early Saturday morning -- no word yet on a name.

Our advice to Khloe? ... Be careful with those nails around the newborn.