I like chatting while walking on the beach.

Literal

Beach [at-で] chatting [while-ながら] strolling [nominalizer-の] [subject-が] like.

ながら connects two simultaneous actions — chatting while walking. おしゃべりしながら散歩する is nominalized with の and marked with が as the object of 好き. A natural expression of a simple pleasure.