Go back another four hundred years to Old English and Beowulf and it becomes complete gobbledygook (to me at least).
What's really fun is that if you keep the dialect in your head, and try reading it out loud with your best "Chaucer accent" it feels like slipping on a pair of glasses: you immediately "get" stuff that you'd have thought was impenetrable just looking at the page.
Source: my medieval lit classes, with a teacher who was really good.
Also: only reading the "boring" bits. When I was in high school I was excused English classes (took English 101 at the local college instead - told you I was a nerd), but overheard my classmates hating their way through "The Wife of Bath's Tale", or "The Knight's Tale" - one of those - and introduced them (nerd!) to "The Miller's Tale" - broad scatalogical comedy - which they loved. Later I did something similar for them with Gulliver's Travels, by showing them the bit where he has fairly graphic sex with the giantess. (I think that's an actual kink, but I certainly didn't know that at the time!)