HIKME is an acronym for "Ha! I kill me!" It is used in internet chat and text message lingo in a similar way to "lol" ("laughing out loud").
A variation on this is HYKME for "Ha! You kill me!"
"Ha! I kill me!" is one of ALF's most well-known catch phrases. He often says this while slapping his hand on the table, after telling a joke. Rumor has it that Alex Adam created this catch phrase back on Melmac.