The neighbor's chicken is better than your own.

Literal

Neighbor [of-の] chicken [topic-は] own [of-の] chicken [than-に] surpasses.

A proverb with the 'grass is greener' vibe. まさる ('to surpass, be better than') is a literary comparative verb, takes に on what is surpassed. The kanji 鶏 ('chicken') is the same for the bird and the dish. Proverb register with classical flavor.