I’m having trouble confirming this reference and engravement CHG and would greatly appreciate some assistance from you. May movement photos would help so i opened it. My research thus far leads me to nowhere . I’m also having trouble with the 27389 as it’s not a tipical serial no. Engravement but same typo and size as ‘CHG’ or similar. f you check omega Serial number refers to 1968 What Can be valid. Any other input is appreciated from the experts.

 

It's simply a personal engraving and only CHG knows the meaning of 27389.
It could be a military service number, his mistress' phone number, his secret Swiss bank account number, the genetic ID for Dusp13 dual specificity phosphatase 13 [ Mus musculus (house mouse) ].................

Only CHG can tell you.