Yes, Saul was chosen by God.
1 Sam 9:17) And when Samuel saw Saul, the LORD said unto him, Behold the man whom I spake to thee of! this same shall reign over my people.
1 Sam 10:1) Then Samuel took a vial of oil, and poured
it upon his [Saul's] head, and kissed him, and said,
Is it not because the LORD hath anointed thee
to be captain over his inheritance?
1 Sam 15:11) It repenteth me [the LORD] that I have set up Saul
to be king: for he is turned back from following me, and hath not performed my commandments. And it grieved Samuel; and he cried unto the LORD all night.