There are no perfect rhymes for “chien” in English, as it is a French word. However, you can find near rhymes or slant rhymes:
Near rhymes
* keen
* seen
* lean
Slant rhymes
* chain
* brain
* gain
These words have similar vowel sounds but different consonant sounds, which can still create a sense of rhyme.
It is important to note that these rhymes are only effective if you are using “chien” in a context where it is understood to be French.