  Theoretical models of stellar evolution predict that most of the lithium
inside a star is destroyed as the star becomes a red giant. However,
observations reveal that about 1% of red giants are peculiarly rich in lithium,
often exceeding the amount in the interstellar medium or predicted from the Big
Bang. With only about 150 lithium-rich giants discovered in the past four
decades, and no distinguishing properties other than lithium enhancement, the
origin of lithium-rich giant stars is one of the oldest problems in stellar
astrophysics. Here we report the discovery of 2,330 low-mass (1 to
3$\,M_\odot$) lithium-rich giant stars, which we argue are consistent with
internal lithium production that is driven by tidal spin-up by a binary
companion. Our sample reveals that most lithium-rich giants have helium-burning
cores ($80^{+7}_{-6}\%$), and that the frequency of lithium-rich giants rises
with increasing stellar metallicity. We find that while planet accretion may
explain some lithium-rich giants, it cannot account for the majority that have
helium-burning cores. We rule out most other proposed explanations as the
primary mechanism for lithium-rich giants, including all stages related to
single star evolution. Our analysis shows that giants remain lithium-rich for
only about two million years. A prediction from this lithium depletion
timescale is that most lithium-rich giants with a helium-burning core have a
binary companion.
