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, $H_{ctext{2}}(T)$, of CaKFe$_{4}$As$_{4}$ was determined up to 630 kOe. The anisotropy parameter $gamma(T)=H_{ctext{2}}^{perp}/H_{ctext{2}}^{|}$, 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 $dH_{ctext{2}}^{|}/dTsimeq-44$ kOe/K and $dH_{ctext{2}}^{perp}/dT simeq-109$ 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 $H_{ctext{2}}^{perp}(0)$ can be extrapolated to $simeq 920$ kOe, well above the BCS paramagnetic limit.
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