"Tier" would be an animal of sorts. "chen" is a common suffix for cutiefying something or indicate it's small (and adorable).
"Tierchen" would be a cute animal, usually a small one too.
The suffixes "-lein" und "-erl" function similarly but have been largely replaced in common german (though in southern germany, both are alive and well)
It is the "-lein" in "Fräulein", but "-lein" isn't only for feminine nouns: the word "Männlein" also exists. I suspect "-erl" is the same, though I don't speak a dialect where it's used; some dialects have "-l" or "-li" which can also attach to any gender of noun (as in "Hansl" and "Gretl")