The first measurement of vector-boson production associated with a top quark-antiquark pair in proton-proton collisions at $\sqrt{s}=7\text{ }\text{ }\mathrm{TeV}$ is presented. The results are based on a data set corresponding to an integrated luminosity of $5.0\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$, recorded by the CMS detector at the LHC in 2011. The measurement is performed in two independent channels through a trilepton analysis of $t\overline{t}Z$ events and a same-sign dilepton analysis of $t\overline{t}V$ ($V=W$ or $Z$) events. In the trilepton channel a direct measurement of the $t\overline{t}Z$ cross section ${\ensuremath{\sigma}}_{t\overline{t}Z}={0.28}_{\ensuremath{-}0.11}^{+0.14}\text{ }(\mathrm{stat}{)}_{\ensuremath{-}0.03}^{+0.06}\text{ }(\mathrm{syst})\text{ }\text{ }\mathrm{pb}$ is obtained. In the dilepton channel a measurement of the $t\overline{t}V$ cross section yields ${\ensuremath{\sigma}}_{t\overline{t}V}={0.43}_{\ensuremath{-}0.15}^{+0.17}\text{ }(\mathrm{stat}{)}_{\ensuremath{-}0.07}^{+0.09}\text{ }(\mathrm{syst})\text{ }\text{ }\mathrm{pb}$. These measurements have a significance, respectively, of 3.3 and 3.0 standard deviations from the background hypotheses and are compatible, within uncertainties, with the corresponding next-to-leading order predictions of ${0.137}_{\ensuremath{-}0.016}^{+0.012}$ and ${0.306}_{\ensuremath{-}0.053}^{+0.031}\text{ }\text{ }\mathrm{pb}$.