Chdi and Chwi are alternative forms of Ti and Chi. You might come across them in the dialect of Gwynedd (north-west Wales), for example, or sometimes in the more formal registers of Welsh.
I asked this question in another thread and someone said it's a variation of 'ti' used almost exclusively in the North:
ti vs. chi
EDIT: Say Something in Welsh just mentioned this in the intermediate course, it seems to be used in places where you'd use 'fo'/'fi', ie. after a vowel. Efo chdi, i chdi, etc. I must say that it feels really nice to say, especially after 'efo'.
How different are the dialects of Welsh in comparison to English dialects? Does it amount to the amount of difference between north American English and traditional Doric Scots?