He won the Nobel for his development of a method called phage display, in which a virus that infects bacteria can be used to evolve new proteins.
Smith, speaking to The Associated Press after learning about this Nobel win, credited others for the work that led to his breakthrough.
He built up a collection of phages, with billions of antibody varieties on their surface, and engineered them make them more effective.
Professor Allison is the "Vivian L. Smith Distinguished" Chair of the Department of Immunology, and Director of the Parker Institute for Cancer Immunotherapy at the University of Texas' MD Anderson Cancer Center in Houston, USA.
Dr Smith said he learned of the prize in a pre-dawn phone call from Stockholm.
USA scientists Frances Arnold and George Smith and British researcher Gregory Winter won the Nobel Chemistry Prize on Wednesday, October 3, for applying the principles of evolution to develop enzymes used to make everything from biofuels to medicine.
"What always amazes me about Frances is she's such a powerhouse - she gets so much done", said Michael Hecht, a professor of chemistry at Princeton and a longtime friend of Arnold.
"I hope that my getting this prize will highlight the fact that, yes, women can do this, they can do it well and that they can make a contribution to the world and be recognized for it", Arnold said in an email. "Yes, I am in favor of making sure we do as much as we can for our successful faculty". But we'll think hard how we'll do it.
Scientists Frances Arnold, George Smith and Gregory Winter won the 2018 Nobel Prize for Chemistry for research using directed evolution to produce enzymes and antibodies for new chemicals and pharmaceuticals, the award-giving body said on Wednesday. "It's not just the money, it has a meaning well-beyond the money".
Aston Martin shares tumble after London float
On 1 October the price range was narrowed even more to between £18.50 ($24.03) and £20 ($25.98). It sold 5,117 cars in 2017, while revenue grew 8 percent in the first half this year.
Arthur Ashkin, of the United States, was awarded half the nine million kronor (£770,000) prize, with the other half shared by Gerard Mourou of France and Canadian Donna Strickland. And a lot of her work has benefits in life sciences, apart from applications in biofuels, and dozens of other applications.
The other half of the prize will be shared by George Smith of the University of Missouri and Gregory Winter of the MRC Laboratory in Cambridge. Smith realised that this could be handy: for example if it wasn't known what protein a particular gene gave rise to, it could be put into a phage and the mystery protein would appear on the surface and could be identified.
The winners will each receive a share of the SEK9 million (£771,000) prize, and will go to Stockholm to receive their prize medals from the King of Sweden at a ceremony on 10 December.
With two Nobel prize winners in as many days, women scientists have welcomed the research community "waking up" to the feats of their female peers, but insist they remain underpaid and undervalued compared to men.
A University of Missouri professor has been awarded a Nobel Prize.
The victor of the Nobel Peace Prize is to be announced Friday.
These scientists were selected for their groundbreaking inventions in the field of laser physics. 8 October in Stockholm will name the victor of the prize for Economics in memory of Alfred Nobel.