There exists a myth that Bill Hamilton was the first to coin the term “selfish gene” as a way of expressing the gene-centred view of evolution.
This is untrue.
This myth is based on the observation that Bill Hamilton used the term “selfish gene” before publication of Richard Dawkins’ book “The Selfish Gene”. 
Did Bill use the term "selfish gene" before Richard?
Yes. Almost certainly.
Did Bill “coin the term “selfish gene” as a way of expressing the gene-centred view of evolution"?
Instead, Bill and others used the term in describing how a "selfish gene" might spread rapidly in a population of individuals carrying an "altruistic gene" and mechanisms by which an altruistic gene might persist in a population of selfish genes. 
To understand the debate we need some context.
At the time altruistic behaviours posed a major problem for evolutionary theory.
There was significant interest in how “altruistic genes” could possibly prevail in a population.
In a Darwinian world of "survival of the fittest", how could altruistic behaviours ever emerge?
The discussion on the conference circuit used the notion of a “selfish gene” to explore mechanisms by which apparently altruistic behaviours might arise in a population of selfish genes.
Bill Hamilton, John Maynard Smith, Bob Trivers and George Williams identified mechanisms by which such "altruistic" genes might evolve – through kin selection, games theory, reciprocal altruism and others.
In the extreme form, some of these mechanisms invoked what was, at the time, the heretical notion of inclusive fitness.
The idea that by sacrificing myself I ensure other copies of my genes persist in other individuals – even though I as an individual might perish.
Thus the altruistic gene survives by maximizing its own inclusive fitness.
The altruistic gene is itself a selfish gene.
Richard Dawkins’ book “The Selfish Gene” made this explicit.
 This is the original version of the Wikipedia entry http://en.wikipedia.org/wiki/TheSelfish_Gene prior to March 20, 2013. On that date some well-intentioned but misguided Wikipedia contributor amended the word coined to used suggesting incorrectly – see the History page - that Bill Hamilton and not Richard Dawkins first coined the term as a way of expressing the gene-centred view of evolution. This is untrue – see above.
 Hamilton WD 1971 Selection of selfish and altruistic behaviour in some extreme models. In, Man and Beast: Comparative Social Behavior, Eisenberg JF, Dillon WS (Eds) Smithsonian Institution Press:Washington. Anyone reading this chapter will be aware that the single use of the phrase “selfish gene” is in the context of a broader discussion of the population dynamics of such a gene. The phrase is used to explore mechanisms rather than as a way of expressing the gene-centred view of evolution.