"You chicken. Me Tarzan."

The boys have found a rope hanging from a branch of a tree across the river. They refer to it as a Tarza ie a Tarzan rope.

Tarzan by Edgar Rice Burroughs
Public Domain
Tarzan of the Apes was created by Edgar Rice Burroughs in 1912 originally for magazine publication, with the novel coming out in 1914. Tarzan is a British lord, John Clayton or Viscount Greystoke who is marooned on the West Coast of Africa by mutineers at the age of one. Having lost his parents, he is brought up by apes. Twenty years later he meets and falls in love with an American Jane Porter when she becomes marooned at the same spot on the coast. Among other adventures, they return to England to marry, where Tarzan is disillusioned by the hypocrisy and greed of 'civilised' society.

The boys in the story are more likely to have come across Tarzan from the screen rather than off the page. Tarzan films started as early as 1918, in the silent era. The actor who played Tarzan in the period covered by the stories was Gordon Scott (1955-1960) and yet, mainly because of Saturday morning TV repeats, the boys would have been most familiar with the most popular Tarzan of all time, Johnny Weismuller, the five-times Gold medal swimming champion, who played Tarzan from 1932 to 1949.

Here is Johnny Weismuller's famous Tarzan cry.

 

And here is the famous meeting between Tarzan and Jane, with the 'Me Tarzan, you Jane' exchange adapted by Palmer in the quote above.