  Detailed chemical abundance distributions for fourteen elements are derived
for eight high-probability stellar members of the solar metallicity old open
cluster M67 with an age of $\sim$4 Gyr. The eight stars consist of four pairs,
with each pair occupying a distinct phase of stellar evolution: two G-dwarfs,
two turnoff stars, two G-subgiants, and two red clump K-giants. The abundance
analysis uses near-IR high-resolution spectra ($\lambda$1.5 -- 1.7$\mu$m) from
the APOGEE survey and derives abundances for C, N, O, Na, Mg, Al, Si, K, Ca,
Ti, V, Cr, Mn, and Fe. Our derived stellar parameters and metallicity for
2M08510076+113115 suggest that this star is a solar-twin, exhibiting abundance
differences relative to the Sun of $\leq$ 0.04 dex for all elements. Chemical
homogeneity is found within each class of stars ($\sim$0.02 dex), while
significant abundance variations ($\sim$0.05 -- 0.20 dex) are found across the
different evolutionary phases; the turnoff stars typically have the lowest
abundances, while the red clump tend to have the largest. Non-LTE corrections
to the LTE-derived abundances are unlikely to explain the differences. A
detailed comparison of the derived Fe, Mg, Si, and Ca abundances with recently
published surface abundances from stellar models that include chemical
diffusion, provides a good match between the observed and predicted abundances
as a function of stellar mass. Such agreement would indicate the detection of
chemical diffusion processes in the stellar members of M67.
