In their first abortion case rulings, conservative justices Neil Gorsuch and Brett Kavanaugh, President Donald Trump's appointments, were in the minority, voting to uphold the Louisiana law that would have overturned a 2016 ruling by a different group of court justices that struck down an nearly identical restrictive abortion law in Texas.
The law required that doctors providing abortions have admitting privileges to nearby hospitals, which the justices said led to an undue burden on women.
Were this Court to again face the question decided by Roe in 1973-whether the Constitution protects women from government interference in abortion as a matter of substantive due process-Roberts could well apply the same logic to justify leaving Roe and the numerous cases that applied it alone.
The 2014 Louisiana law said that doctors must hold privileges at hospitals within 30 miles (48km) of their practice - which the state argued was to protect women's health.
In dissent, Justice Clarence Thomas wrote, "Today a majority of the Court perpetuates its ill-founded abortion jurisprudence by enjoining a perfectly legitimate state law and doing so without jurisdiction".
You would think one ruling of the Supreme Court in 2016 would be enough to discourage abortion opponents from passing a law identical to the one the court threw out. The Louisiana law burdens women seeking pre-viability abortions to the same extent as the Texas law, according to factual findings that are not clearly erroneous.
The chief justice today joined with the four liberals on the court to strike down the Louisiana statute.
Instead, Roberts said that he was not prepared to reverse the precedent set by the court's 2016 decision - made before Trump's justices arrived - rejecting an identical Texas law.
Read the Supreme Court's full decision, including a summary of the case, the opinions by Breyer and Roberts, and dissents from Thomas, Samuel Alito, Neil Gorsuch and Brett Kavannaugh, below.
"With this win, the clinics in Louisiana can stay open to serve the one million women of reproductive age in the state", she said in a statement.
But abortion-rights supporters cited the rarity of the need for hospitalization after an abortion and said women could, if needed, be hospitalized whether their abortion practitioner had admitting privileges or not. It followed by only two weeks a watershed, 6-3 decision in which the high court supported gay and transgender rights by ruling longstanding, non-discrimination protections in federal workplace law cover "sexual orientation" and "gender identity".
Chief Justice Roberts' vote was a bit of a surprise because he voted in the Texas case to uphold the clinic restrictions. And pro-lifers will see that even though a conservative-leaning Court on balance upholds more restrictions than a progressive-leaning Court would, the fundamental framework of Roe will not be overturned.
Since the decision in the Texas case, President Trump has nominated Gorsuch to replace the late Antonin Scalia, who died in 2016 before that ruling.
In that decision, now-retired justice Anthony Kennedy joined the court's four liberals to form a majority.