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Electron affinity of chlorine = -349 kJ per mole. And, first ionization energy of sodium = 496 kJ per mole while energy required for combining= 147 kJ per mole.
Isn't it a contradiction against genereal physics and G.N. Lewis' "electronic theory of valency"?
The Born-Haber Cycle might help you visualizing how those values are used. Notice the values used bellow are a bit different from the ones you got.
Electron affinity
The amount of energy released when an electron is added to a neutral atom or molecule to form a negative ion.
Ionization energy
The amount of energy required to remove an electron from the atom.
Enthalpy of formation (ΔH)
The change of enthalpy that accompanies the formation of 1 mole of the compound from its elements.
Your question assumes that there is a total transfer of an electron from sodium to chlorine when some kind of sodium chloride compound is formed.
The problem is that in compound formation there is never a total transfer of an electron from one atom to another. In other words while there are pure covalent compounds (electrons completely shared) there are no pure ionic bonds (electron totally transferred.)
In addition, as the other answers have indicated, the nature of the final compound also has an influence. In solid sodium chloride a network of shared electrons is formed linking many sodium and chloride atoms together. In gaseous sodium chloride, $\ce{NaCl}$ there are only the two atoms present. In sodium chloride solutions the situation is even more complex.
