in this talk, we study the chow group of the motive associated to a tempered global l-packet $\pi$ of unitary groups of even rank with respect to a cm extension, whose global root number is -1. we show that, under some restrictions on the ramification of $\pi$, if the central derivative $l'(1/2,\pi)$ is nonvanishing, then the $\pi$-nearly isotypic localization of the chow group of a certain unitary shimura variety over its reflex field does not vanish. this proves part of the beilinson--bloch conjecture for chow groups and l-functions. moreover, assuming the modularity of kudla's generating functions of special cycles, we explicitly construct elements in a certain $\pi$-nearly isotypic subspace of the chow group by arithmetic theta lifting, and compute their heights in terms of the central derivative $l'(1/2,\pi)$ and local doubling zeta integrals. this is a joint work with chao li.