  We report an {\it in-situ} scanning tunneling microscopy study of atomically
thin films of CeCoIn$_5$, a $d$-wave heavy-fermion superconductor. Both
hybridization and superconducting gaps are observed even in monolayer
CeCoIn$_5$, providing direct evidence of superconductivity of heavy
quasiparticles mediated by purely two-dimensional bosonic excitations. In these
atomically thin films, $T_c$ is suppressed to nearly half of the bulk, but is
similar to CeCoIn$_5$/YbCoIn$_5$ superlattices containing CeCoIn$_5$ layers
with the same thickness as the thin films. Remarkably, the out-of-plane upper
critical field $\mu_0H_{c2\perp}$ at zero temperature is largely enhanced from
those of bulk and superlattices. The enhanced $H_{c2\perp}$ well exceeds the
Pauli and bulk orbital limits, suggesting the possible emergence of unusual
superconductivity with parity mixing caused by the inversion symmetry breaking.
