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We present spectroscopic and photometric monitoring of NGC 3783 conducted throughout the first half of 2020. Time delays between the continuum variations and the response of the broad optical emission lines were clearly detected, and we report reverberation measurements for H$β$, HeII $λ4686$, H$γ$, and H$δ$. From the time delay in the broad H$β$ emission line and the line width in the variable portion of the spectrum, we derive a black hole mass of $M_{\rm BH} = 2.34^{+0.43}_{-0.43} \times 10^7$ M$_{\odot}$. This is slightly smaller than, but consistent with, previous determinations. However, our significantly improved time sampling ($T_{\rm med}=1.7$ days compared to $T_{\rm med}=4.0$ days) has reduced the uncertainties on both the time delay and the derived mass by $\sim 50$%. We also detect clear velocity-resolved time delays across the broad H$β$ profile, with shorter lags in the line wings and a longer lag in the line core. Future modeling of the full velocity-resolved time delay response will further improve the reverberation-based mass for NGC 3783, adding it to the small but growing sample of AGNs for which we have direct, primary black hole mass measurements. Upcoming MUSE observations at VLT will also allow NGC 3783 to join the smaller sample of black holes where reverberation masses and masses from stellar dynamical modeling may be directly compared.