===Louisiana Supreme Court===
In the nonpartisan blanket primary held on September 21, 1996, Traylor as a Republican unseated the [[Democratic Party|Democrat]] Joe Bleich of [[Ruston, Louisiana|Ruston]] to win a ten-year term on state Supreme Court. Traylor polled 60,484 votes (53 percent) to Bleich's 53,098 (47 percent). Bleich, a former state representative, had served on the court since 1983.<ref>Louisiana Secretary of State, Election Returns, September 21, 1996.</ref>
In 2006, Traylor was unopposed for a second term on the court, but he left the position two and a half years later. Marcus R. Clark, a Calcasieu Parish, native and a state district judge from Monroe, then won a [[special election]] in the fall of 2009 to complete Traylor's term, which expired January 1, 2017.<ref>Louisiana Secretary of State, Election Returns, September 30, 2006</ref>
In the 2000 case of ''State v. Smith'',<ref>''State v. Smith'' 766 So. 2d 501 (La., 2000)</ref> Justice Traylor embraced the view of [[judicial restraint]] in authoring the Supreme Court's opinion upholding the constitutionality of the Louisiana "crime-against-nature" statute.<ref name=bepress>[http://www.lambdalegal.org/news/pr/louisiana-supreme-court.html] [http://www.glapn.org/sodomylaws/usa/louisiana/laeditorials001.htm Chet Traylor on Louisiana's "crime-against-nature" statute], glapn.org; accessed June 28, 2015.</ref> In his decision, Traylor ruled that the state constitution must not be manipulated by transient majorities of the judges. Such a view, he said, would create a government by judicial fiat, instead of a constitutional system. "Disaffected groups unable to obtain legislative redress need only convince a majority of this court that what they seek is an implicit 'right' afforded by the Louisiana Constitution. Our constitution wisely provides for separation of powers, and authorizes the legislature to make public policy determinations in this area," Traylor said.<ref name=bepress/> Traylor said that the state constitution does not protect "immoral acts ... Simply put, commission of what the legislature determines as an immoral act, even if consensual and private, is an injury against society".<ref>{{cite web|url=http://www.qrd.org/qrd/www/legal/lgln/09.00.html|title=Queer Resources Directory|publisher=qrd.org|accessdate=July 10, 2010}}</ref>
In 2007, in ''Cook v. Cook,'' Traylor concurred in the majority opinion of the Supreme Court that a mother who exposed her children to her [[lesbian]] relationship was not entitled to custody of those children.<ref>''Cook v. Cook'' 970 So. 2d 960 (La., 2007)</ref> That same year in ''State v. Bailey (2007)'', Traylor concurred with the majority in the so-called Jena 6 case that concluded that a white district attorney in LaSalle Parish should have recused himself from prosecution of the six [[African American]] high school students who attacked a white classmate because the DA's past behavior showed an unwillingness to prosecute whites for similar crimes.<ref>''State v. Bailey'' 713 So. 2d 588 (La., 2007)</ref>
In 2008, Traylor wrote a unanimous court opinion that upheld the constitutionality of two state laws giving homeowners until the fall of 2007 to file lawsuits or claims against their [[insurance]] companies over damage from [[Hurricane Katrina|Hurricanes Katrina]] and Rita. The court noted that the extension was for one year and was limited to those two storms.<ref>{{cite web|url=http://www.pianet.com/IssuesOfFocus/HotIssues/naturaldisaster/8-30-06-7.htm|title=National Association of Professional Insurance Agents|publisher=pianet.com|accessdate=July 10, 2010}}</ref>