Hidden in Pixels I: Discovery of dual "little red dots" indicates excess clustering on kilo-parsec scales

``Little Red Dots'' (LRDs) are an abundant high-redshift population newly discovered by the James Webb Space Telescope (JWST) and considered to be an early growth phase of supermassive black holes (SMBHs). Using a method of pixel-by-pixel color selection and relaxing the compactness criteria, we identify four dual LRD candidates in the COSMOS-Web survey with projected separations of $0.\!\!^{\prime\prime}2$-$1.\!\!^{\prime\prime}2$. A comparison between existing LRD samples and mock data reveals that the projected separations of these dual LRD candidates are unlikely to result from chance projections of objects at different redshifts. Furthermore, two of the four systems are covered by COSMOS-3D slitless spectroscopy, and a single-line detection at the same observed wavelength for each LRD in a pair strongly supports that they are at identical redshifts. Assuming that the detected lines are H$\alpha$ based on their high equivalent width and broad profile, the spectroscopic redshifts of $z=5.822$ and $5.464$ for the two pairs are consistent with their photometric redshifts, yielding projected separations of $1.64$ and $7.36\,{\rm kpc}$. These discoveries suggest that the angular auto-correlation function (ACF) of LRDs exhibits an excess ($\sim20$-$30$ times) on sub-arcsec (kilo-parsec) separations compared to an extrapolation of a power-law ACF of JWST-found AGNs measured over $10^{\prime\prime}$-$100^{\prime\prime}$. Our sample is likely to represent precursors of mergers between LRDs, and such mergers may be one of the mechanisms that can drive the rapid growth of SMBHs in their early evolutionary stages.