The elliptic azimuthal anisotropy coefficient (upsilon(2)) is measured for charm (D-0) and strange (K-S(0), Lambda, Xi(-), and Omega(-)) hadrons, using a data sample of p + Pb collisions collected by the CMS experiment, at a nucleonnucleon center-of- mass energy of root(NN)-N-s = 8.16 TeV. A significant positive upsilon(2) signal from long- range azimuthal correlations is observed for all particle species in high- multiplicity p + Pb collisions. The measurement represents the first observation of possible long-range collectivity for open heavy flavor hadrons in small systems. The results suggest that charm quarks have a smaller upsilon(2) than the lighter quarks, probably reflecting a weaker collective behavior. This effect is not seen in the larger PbPb collision system at root(NN)-N-s = 5.02 TeV, also presented.