  Single crystalline, single phase CaKFe$_{4}$As$_{4}$ has been grown out of a
high temperature, quaternary melt. Temperature dependent measurements of x-ray
diffraction, anisotropic electrical resistivity, elastoresistivity,
thermoelectric power, Hall effect, magnetization and specific heat, combined
with field dependent measurements of electrical resistivity and field and
pressure dependent measurements of magnetization indicate that
CaKFe$_{4}$As$_{4}$ is an ordered, stoichiometric, Fe-based superconductor with
a superconducting critical temperature, $T_c$ = 35.0 $\pm$ 0.2 K. Other than
superconductivity, there is no indication of any other phase transition for 1.8
K $\leq T \leq$ 300 K. All of these thermodynamic and transport data reveal
striking similarities to that found for optimally- or slightly over-doped
(Ba$_{1-x}$K$_x$)Fe$_2$As$_2$, suggesting that stoichiometric CaKFe$_4$As$_4$
is intrinsically close to what is referred to as "optimal-doped" on a
generalized, Fe-based superconductor, phase diagram. The anisotropic
superconducting upper critical field, $H_{c\text{2}}(T)$, of
CaKFe$_{4}$As$_{4}$ was determined up to 630 kOe. The anisotropy parameter
$\gamma(T)=H_{c\text{2}}^{\perp}/H_{c\text{2}}^{\|}$, for $H$ applied
perpendicular and parallel to the c-axis, decreases from $\simeq 2.5$ at $T_c$
to $\simeq 1.5$ at 25 K which can be explained by interplay of paramagnetic
pairbreaking and orbital effects. The slopes of
$dH_{c\text{2}}^{\|}/dT\simeq-44$ kOe/K and $dH_{c\text{2}}^{\perp}/dT
\simeq-109$ kOe/K at $T_c$ yield an electron mass anisotropy of
$m_{\perp}/m_{\|}\simeq 1/6$ and short Ginzburg-Landau coherence lengths
$\xi_{\|}(0)\simeq 5.8 \text{\AA}$ and $\xi_{\perp}(0)\simeq 14.3 \text{\AA}$.
The value of $H_{c\text{2}}^{\perp}(0)$ can be extrapolated to $\simeq 920$
kOe, well above the BCS paramagnetic limit.
