  We performed near-daily observations on the binary pulsars PSR J0218+4232,
PSR J1518+4904 and PSR J2023+2853 with the Canadian Hydrogen Intensity Mapping
Experiment (CHIME). For the first time, we detected the Shapiro time delay in
all three pulsar-binary systems, using only 2--4 years of CHIME/Pulsar timing
data. We measured the pulsar masses to be $1.49^{+0.23}_{-0.20}$ M$_\odot$,
$1.470^{+0.030}_{-0.034}$ M$_\odot$ and $1.50^{+0.49}_{-0.38}$ M$_\odot$
respectively. The companion mass to PSR J0218+4232 was found to be
$0.179^{+0.018}_{-0.016}$ M$_\odot$. We constrained the mass of the
neutron-star companion of PSR J1518+4904 to be $1.248^{+0.035}_{-0.029}$
M$_\odot$, using the observed apsidal motion as a constraint on mass
estimation. The binary companion to PSR J2023+2853 was found to have a mass of
$0.93^{+0.17}_{-0.14}$ M$_\odot$; in the context of the near-circular orbit,
this mass estimate suggests that the companion to PSR J2023+2853 is likely a
high-mass white dwarf. By comparing the timing model obtained for PSR
J0218+4232 with previous observations, we found a significant change in the
observed orbital period of the system of $\dot{P_{\rm b}} = 0.14(2) \times
10^{-12}$; we determined that this variation arises from ``Shklovskii
acceleration" due to relative motion of the binary system, and used this
measurement to estimate a distance of $d=(6.7 \pm 1.0)$ kpc to PSR J0218+4232.
This work demonstrates the capability of high-cadence observations, enabled by
the CHIME/Pulsar system, to detect and refine general-relativistic effects of
binary pulsars over short observing timescales.
