Why is "Chop Gate" pronounced so strangely?

Solution 1:

It may be because the g in Old English could be pronounced like a y when followed by an e or ea diphthong. For example, middangeard, the term used to refer to "this place right here where people live" (literally "middle earth" — so you can see where Tolkien got the term) was pronounced middahnyaird. The North Yorkshire accent may retain some vestiges of Old English pronunciation.

Solution 2:

Maps aren't written by locals.

For example "Pately Bridge" is known locally as "Pately Brig". Brig being norse for a large rock outcrop - no bridge involved. But some map maker came from the south, asked a local what the place was called and misunderstood the answer.

It's not that "gate" is necessarily pronounced 'yat' - the 'yat' pronunciation is possibly from some totally unrelated earlier word and "gate" is the nearest the official surveyor could come to it (edit apparently in this case yat = gate)

Yorkshire has a wide variety of place names, from early celtic (Pen-y-ghent), mostly Norse, a few anglo-saxon and a scattering of modern Norman places.