Single top quark production in association with a Z boson ($\text{tZq}$) is observed. Proton-proton collision events containing three leptons (electrons or muons) are analyzed. The data correspond to an integrated luminosity of 77.4 $\text{fb}^{-1}$, collected with the CMS detector throughout 2016 and 2017. The analysis is significantly more sensitive than any previous search for $\text{tZq}$ because of the usage of machine learning for lepton identification, and a redesigned search strategy. The observed (expected) signal significance of $\text{tZq}$ is 8.2 (7.7) standard deviations above the background only hypothesis. The $\text{tZq}$ cross section is measured to be $\sigma(\text{pp}\to \text{tZq} \to \text{t}\ell\ell\text{q}) = 111 \pm 13~\text{(stat)}~^{+11}_{-9}~\text{(syst)}~\text{fb}$, with an uncertainty more than twice smaller than that on any previous measurement.