To answer your other question, yes there are still single-cell organisms evolving into new species all the time, in the ocean and elsewhere. That includes new multi-cellular species evolving from single cells all the time. But it takes a long time to develop from cell, to clump of slime, to something with legs. So you might not notice the changes if you aren’t super patient.
Or were those separate questions? Are you asking if chickens descended from single-cell organisms? Yes they did. With a lot of steps in between.