Although it is well established that some extragalactic radio sources are time-variable, the properties of this radio variability, and its connection with host galaxy properties, remain to be explored—particularly for faint sources. Here we present an analysis of radio variable sources from the CHILES Variable and Explosive Radio Dynamic Evolution Survey (CHILES VERDES)—a partner project of the 1.4 GHz COSMOS H i Large Extragalactic Survey. CHILES VERDES provides an unprecedented combination of survey depth, duration, and cadence, with 960 hr of 1–2 GHz continuum VLA data obtained over 209 epochs between 2013 and 2019 in a 0.44 deg$^{2}$ section of the well-studied extragalactic deep field, COSMOS. We identified 18 moderate-variability sources (showing 10%–30% flux density variation) and 40 lower-variability sources (2%–10% flux density variation). They are mainly active galactic nuclei (AGNs) with radio luminosities in the range of 10$^{22}$–10$^{27}$ W Hz$^{−1}$, based on cross-matching with COSMOS multiwavelength catalogs. The moderate-variability sources span redshifts z = 0.22–1.56, have mostly flat radio spectra (α > −0.5), and vary on timescales ranging from days to years. The lower-variability sources have similar properties, but generally have higher radio luminosities than the moderate-variability sources, extending to z = 2.8, and have steeper radio spectra (α < −0.5). No star-forming galaxy showed statistically significant variability in our analysis. The observed variability likely originates from scintillation on short (∼week) timescales, and Doppler-boosted intrinsic AGN variability on long (month–year) timescales.