IIRC, his leg was sore {or injured} so he limped and the powers that be liked it, so Chester limped for the whole series.
Internet movie database says he did it to be noticed.:
Gave his character Chester on Gunsmoke a bad leg and a limp out of fear that he would not be noticed when playing scenes with the 6' 9" James Arness unless his character had an unusual trait that would call attention to him.Almost didn't get the part of Chester Goode on "Gunsmoke" until he asked for a second chance to read the lines in a humorous, countrified accent and won the role.