Is anyone here familiar with this language? (Or is it a dialect?)
I can read it without too much difficulty.
Strictly speaking it could be described as a stage, or historical phase, of the English language. 1100 - 1500 is conventionally taken as its span. Just as English today has its own dialects, so did ME. Some of them are easier for modern readers to understand; for example, Chaucer wrote in the dialect which was to contribute most to the way in which English is spoken and written today, so is reasonably easy to understand.
Here’s the opening of the Canterbury Tales:
Whan that Aprille with his shoures sote
The Droghte of Marche hath perced to the rote,
And bathed every veyne in swich licour,
Of which vertu engendred is the flour;
Whan Zephirus eek with his swete breeth
Inspired hath in every holt and heeth
The tendre croppes, and the yonge sonne
Hath in the Ram his halfe course y-ronne,[…]
You will see that there are some weird spellings, and word order is sometimes different, and word meanings have sometimes shifted, but otherwise it is not too difficult to decode - go on, have a go! 
If you would like to hear a reconstruction of what these lines sounded like,
go to http://eee.uci.edu/programs/medieval/meclips.html
Here’s the opening of Langland’s Piers Plowman, in a dialect more northern than Chaucer’s London one, and perhaps slightly more difficult for us modern folk:
In a somer seson, whan softe was the sonne,
I shoop me into shroudes as I a sheep were,
In habite as an heremite unholy of werkes,
Wente wide in this world wondres to here.
Ac on a May morwenynge on Malverne hilles
Me bifel a ferly, of Fairye me thoghte.
I was wery forwandred and wente me to reste
Under a brood bank by a bourne syde;
And as I lay and lenede and loked on the watres,
I slombred into a slepyng, it sweyed so murye.
Thanne gan I meten a merveillous swevene –
That I was in a wildernesse, wiste I nevere where.
Perhaps even more difficult for us is the dialect of what are called (insultingly) “the Scottish Chaucerians”. Here’s William Dunbar, with the first few lines of his The tretis of the twa mariit women and the wedo :
Apon the Midsummer evin, mirriest of nichtis,
I muvit furth allane, neir as midnicht wes past,
Besyd ane gudlie grein garth, full of gay flouris,
Hegeit, of ane huge hicht, with hawthorne treis;
Quhairon ane bird, on ane bransche, so birst out hir notis
That never ane blythfullar bird was on the beuche harde:
Quhat throw the sugarat sound of hir sang glaid,
And throw the savour sanative of the sueit flouris,
I drew in derne to the dyk to dirkin efter mirthis;
The dew donkit the daill and dynnit the feulis.
Dunbar can be quite coarse. Here’s a bit from his attack on his colleague Kennedy:
Iersche brybour baird, vyle beggar with thy brattis,
Cuntbittin crawdoun Kennedy, coward of kynd,
Evill-farit and dryit as Denseman on the rattis,
Lyk as the gleddis had on thy gulesnowt dynd,
Mismaid monstour, ilk mone owt of thy mynd,
Renunce, rebald, thy rymyng, thow bot royis.
I won’t attempt to translate it! Were I to do so, I think the Forum software’s “rude word censor” would have a field day!
Hi Phylax, I think the main concern would be the words with changed meanings.
I understand that the Canterbury Tales are written in iambic pentameter, but Piers Plowman was written in alliterative verse? (That might make it difficult, considering that we’re unlikely to spot the lifts immediately).
What are the other two in?
Hi, Eureka!
Gosh, I never really thought about the verse forms of the bits I quoted! 
I’ll have to get back to you on that one when I have done some delving. 
So far as the shifted word meanings are concerned, a good dictionary which cites usages of words historically (such as the OED) is a great help. Often the context of the word makes it easier to figure out what the meaning of the word was, if it appears to differ from its present meaning. Also, decent editions of ME texts usually give glosses, often as footnotes, to difficult words and faux-amis.
Hi Eureka, hi Phylax,
I have been reading Middle English on my own for several years and have found the textbook by J.A. Burrow and Thorlac Turville-Petre to be especially useful. It is entitled “A Book of Middle English (second edition)”, and can be easily ordered on Amazon. In terms of what Phylax was saying about dialectical variation in ME, the book gives a wide range of sample readings that really show the breadth of differences in the language. The alliterative verse of the Gaiwan poet, for instance, is much closer to Old English forms than Chaucer’s couplets, and even the short passages provided as readings serve to highlight the transition between the two.
In general, Middle English strikes me as pretty readable from the outset, but I have found that having a formal grammar has really helped me to understand the precise ways in which English evolved. Old English, on the other hand, I studied for quite some time before being able to simply pick up a book and enjoy it…
Hope this proves helpful
Hi, Philokalos!
That’s most excellent advice!
Am I right in thinking you are new to this august forum? If that be the case, may I extend my most cordial welcome to you, and my hopes that you will enjoy it as much as I do.
Phylax
Yes, χαῖρε, ω} φιλοκαλέ.