By chance - Accidentally, or as it happened. It means that he did not do it with a “design” to aid the man that was wounded.
A certain priest - It is said that not less than 12,000 priests and Levites dwelt at Jericho; and as their business was at Jerusalem, of course there would be many of them constantly traveling on that road.
When he saw him - He saw him lie, but came not near him.
Passed by on the other side - On the farther side of the way. Did not turn out of his course even to come and see him.