We investigate the decay
B
+
→
J
/
ψ
ϕ
K
+
in a search for the
X
(
4140
)
state, a narrow threshold resonance in the
J
/
ψ
ϕ
system. The data sample corresponds to an integrated luminosity of
10
.
4
 
 
fb
−
1
of
p
¯
p
collisions at
√
s
=
1.96
 
 
TeV
collected by the D0 experiment at the Fermilab Tevatron collider. We observe a mass peak with a statistical significance of 3.1 standard deviations and measure its invariant mass to be
M
=
4159
.
0
±
4.3
(
stat
)
±
6.6
(
syst
)
 
 
MeV
and its width to be
Γ
=
19
.
9
±
12
.
6
(
stat
)
+
3.0
−
8.0
(
syst
)
 
 
MeV
.