Mr Chisholm gave his support in a letter to the College of Physicians
Two former Labour health ministers have broken ranks with the party over government proposals for minimum alcohol pricing in Scotland.
Malcolm Chisholm and Susan Deacon said they both supported the SNP policy, which Labour will vote against.
Scottish Health Secretary Nicola Sturgeon said setting a minimum price would reduce consumption and harm.
However Labour, and other opposition parties, said the proposal was ill thought out and possibly illegal.
Mr Chisholm expressed his support for the proposal, one of several measures brought forward in the Alcohol Bill, in a letter to the Royal College of Physicians.
He wrote: "I believe that a range of measures must be taken to combat the serious problems caused by alcohol in Scotland.
"I believe that price is a key element and I am persuaded by the arguments in favour of minimum pricing."
The BBC understands Mr Chisholm intends to vote for the policy in parliament - but the SNP government needs the support of another 17 opposition MSPs to win Holyrood approval.
The SNP plans aim to set minimum prices for a unit of alcohol
Ms Deacon, who stood down as an MSP at the last election, told BBC Scotland's Politics Show: "I think minimum pricing is the right way to go.
"There's work to be done to work out precisely what legislation could and should look like, but I would like to see parties coming together - particularly those who say they support measures on minimum pricing - to actually come up with the right arrangement through due process in the parliament."
Ms Deacon added: "Frankly, the Labour party in Scotland has ended up in the wrong place for the wrong reasons on this issue."
But Labour, the Tories and Liberal Democrats, raised concern that minimum pricing was illegal under European competition law and that the policy would fail to target certain "problem drinks".
Other key parts of the bill, which includes proposals to ban drink promotions, powers for licensing boards to raise the age for buying drink from 18 to 21 and a "social responsibility fee" for retailers who sell alcohol, are likely to win approval.