Attempts to unsplit the infinite (to quietly enter) in the following sentence don't seem to succeed:

The queen told the page to quietly enter the chamber where the king was sleeping.

Consider the possibilities:

• The queen told the page quietly to enter the chamber where the king was sleeping.
  Misleading at best. The likely interpetation will be that the queen was speaking quietly.
   
• The queen told the page to enter quietly the chamber where the king was sleeping.
  Pretty awkward. Adverbs do not usually go between verbs and their objects. Who ever says, "I entered quietly the chamber"?
   
• The queen told the page to enter the chamber quietly where the king was sleeping.
  Solved a phony problem and created a real one. Now we've split a relative adverb ("where") from the noun it modifies ("the chamber").
   
• The queen told the page to enter the chamber where the king was sleeping quietly.
  Not even ambiguous. This will be interpreted to mean the king wasn't snoring for a change.

Dick Veit