2 of 2 deleted 24 characters in body

Pylongolf2, 11 bytes

1r1=?1>~<¿

Explanations:

1           push 1 to the stack
 r          pick a random number between 0 and 1
  0=        push 1 to the stack and compare them
    ?1>~<¿  if true, push 1 to the stack then print it forever.
            terminate