A formulation is presented for the calculation of the excess chemical potential mu(ex)(n(test)) of n(test)-mer chains mixed at infinite dilution with a bulk n-mer fluid and of the excess segmental chemical ex potential mu(seg)(ex)=mu(ex)(n + 1) - mu(ex)(n) from detailed atomistic simulations. The formulation is applied for n(test) = 6 to 16 in n-hexadecane (C-16, n = 16) in the liquid (P = 50 atm) and vapor (P = 1.02 atm) states at T = 580 K using a configurational bias Monte Carlo (MC) scheme. Two different reference states (ideal gas and continuous unperturbed chains) are examined for the definition of mu(ex), and simulations are conducted with two united-atom model representations from the recent literature. In parallel, mu(ex) and mu(seg)(ex) with reference to the ideal gas are derived from two cubic equations of state (EoS) for the same systems and conditions. Both the MC and the EoS calculations for both models and reference states examined give a linear dependence of mu(ex)(n(test)) on n(test), confirming that chemical potentials for long chains can be reliably estimated from small test chain and test segment insertions. This confirmation of the "chain increment ansatz" is of great practical value for phase equilibrium calculations in long-chain systems. Predictions for the structure of the C-16 liquid and vapor are in good agreement with existing experimental and simulation evidence. Chain conformations in the liquid and vapor are indistinguishable from unperturbed and ideal gas chain conformations, respectively. In lower temperature liquids (T = 450 K, P = 20 atm), insertions of long test chains cannot provide adequate sampling, but the chain increment ansatz remains useful for estimating chemical potentials.