Moore's law says that the number of transistors on a chip doubles approximately every two years. The Core i7 Sandy Bridge has ~2.3 billion transistors [1], and measures 434 mm^2 [1]. Silicon has a density of 2.4g/cm^3 [2] or .0024g/mm^3. Silicon's atomic weight is 28 --- meaning ~610^23 atoms of Silicon weigh 28 grams --- which means a single atom weighs 4.710^-23g.
Let us pretend that Si crystals are simple-cubic (they're actually diamond-cubic [3]). In that case, a 1x1x1mm cube of crystal weighs 2.410^-3g == 5.210^19 atoms. The cube root of this number, 3.710^6, is the number of atoms on a side, so the number of atoms on a mm^2 face is 1.410^13.
The chip is 434 mm^2, so the face has about 6.1*10^15 atoms on it, otherwise known as 6 million billion.
For roundness, say we have 2 billion transistors on the chip today. Log_2(6,000,000) == 22.
If Moore's law continues until the year 2053, there would be more transistors than atoms on the surface of the chip :-)
[1] http://www.tomshardware.com/reviews/core-i7-3960x-x79-sandy-...