We present detailed C, O, Na, Mg, Si, Ca, Ti, V, Fe, Zr, Ba, and Eu abundance measurements for 20 red giant branch (RGB) stars in the LMC star cluster NGC 1846 ([Fe/H] = -0.59). This cluster is 1.95 Gyr old and lies just below the supposed lower age limit (2 Gyr) for the presence of multiple populations in massive star clusters. Our measurements are based on high and low-resolution VLT/FLAMES spectra combined with photometric data from HST. Corrections for non-local thermodynamic equilibrium effects are also included for O, Na, Mg, Si, Ca, Fe and Ba. Our results show that there is no evidence for multiple populations in this cluster based on the lack of any intrinsic star-to-star spread in the abundances of Na and O: we place 95 \% confidence limits on the intrinsic dispersion for these elements of
respectively. However, we do detect a significant spread in the carbon
abundances, indicating varying evolutionary mixing occurring on the RGB that
increases with luminosity. Overall, the general abundance patterns for NGC 1846
are similar to those seen in previous studies of intermediate-age LMC star
clusters and field stars.