In common (colloquial) English, "perhaps" and "maybe" are used interchangeably, so if you're mostly only concerned with conversational language, you don't really need to be concerned with those two. "Maybe" is viewed as slightly more casual than "perhaps". "Perchance" is not used nearly as often as the other two. It is more ambiguous than both of them. If you're looking for technicalities: "Perhaps" is more associated with actions. The "-haps" is related to the verb "to happen", indicating that when using "perhaps", you are referring to possibility in response to something that directly has happened, is happening, or will happen. "Perchance" is more ambiguous in that is associated with "chance" (evidently). It indicates possibility in response to something that may happen, but cannot be controlled or predicted. "Maybe" is more associated with states of being. The "-be" is related to the verb "to be", indicating that when using "maybe", you are referring to possibility in response to something that was, is, or will be. I'm sorry if that is difficult to understand. (^ ^;)

'Perhaps' and 'maybe' have the same meaning, and can be used interchangeably. Forget about 'perchance'. It doesn't exist in modern English. The only place you will see it is in texts by Shakespeare and other writers from many centuries ago.