The meaning and origin of the expression: To sleep: perchance to dream: ay, there's the rub

To sleep: perchance to dream: ay, there's the rub

What's the origin of the phrase 'To sleep: perchance to dream: ay, there's the rub'?

This line is from the celebrated 'To be, or not to be' speech in Shakespeare's Hamlet, 1602:

HAMLET:
To be, or not to be: that is the question:
Whether 'tis nobler in the mind to suffer
The slings and arrows of outrageous fortune,
Or to take arms against a sea of troubles,
And by opposing end them? To die: to sleep;
No more; and by a sleep to say we end
The heart-ache and the thousand natural shocks
That flesh is heir to, 'tis a consummation
Devoutly to be wish'd. To die, to sleep;
To sleep: perchance to dream: ay, there's the rub;