A search for the standard model Higgs boson decaying to a charm quark-antiquark pair,
H
→
c
c
¯
, produced in association with a top quark-antiquark pair (
t
t
¯
H
) is presented. The search is performed with data from proton-proton collisions at
s
=
13
TeV
, corresponding to an integrated luminosity of
138
fb
−
1
. Advanced machine learning techniques are employed for jet flavor identification and event classification. The Higgs boson decay to a bottom quark-antiquark pair is measured simultaneously and the observed
t
t
¯
H
(
H
→
b
b
¯
)
event rate relative to the standard model expectation is
0.91
−
0.22
+
0.26
. The observed (expected) upper limit on the product of production cross section and branching fraction
σ
(
t
t
¯
H
)
B
(
H
→
c
c
¯
)
is 0.11 (0.13) pb at 95% confidence level, corresponding to 7.8 (8.7) times the standard model prediction. When combined with the previous search for
H
→
c
c
¯
via associated production with a
W
or
Z
boson, the observed (expected) 95% confidence interval on the Higgs-charm Yukawa coupling modifier,
κ
c
, is
|
κ
c
|
<
3.5
(2.7), the most stringent constraint to date.
