By the way, even though Law & Order tied Gunsmoke for the longest-running, live-action prime-time series, Gunsmoke holds the record (by far) for episodes, with 635. Law & Order was 456. The Simpsons has the record for most years, though it currently is behind in number of episodes.
When the show made the transition from radio to TV, it was completely recast. Oddly enough, the original actor to play Matt Dillon on the radio later became a TV star on another series -- William Conrad, who later played the detective Canon. (Articles suggest that one of the deciding factors to go with a different star was Conrad's weight, that just didn't seem fitting for a Western action series, though Gunsmoke was fairly cerebral in comparison to many other Westerns.) James Arness was recommended for the TV role by, of all people, John Wayne, who also introduced the first episode on camera.
Anyway, this is the full, wonderful Gunsmoke theme. (And happily, it comes during end credits from the early years when Dennis Weaver was still on the show, as the limping deputy,'Chester Goode.'
And as a bonus, here's another version of the Gunsmoke theme. It's little known that the song had words, but it did. And in large part that's what I've remember most, since I found them so particularly wistful, to fit the music so well. It's also can be easier to remember a song when you can sing along. To be honestly I didn't remember all the words -- in fact, very few -- but have always remembered the passage that began, "And if heaven ever let you, you could tell a rugged tale..."
Here are the Prairie Chiefs with the song. And there's Dennis Weaver on the left. Whimsically blocked out by the arrow. (Though once the video begins to play, it all becomes clear.)