The CIELCHuv color space can be rendered here. All colors that are displayable on a typical screen (ie. within sRGB gamut) are drawn with the actual colors. Human-visible colors (ie. within CIE XYZ gamut) are drawn in light grey by default. Invisible or impossible colors are not drawn.
You can use the color picker based on this color space here.
In the CIELCHuv and CIELCHab color spaces, three values or parameters are sufficient to specify any color (that is human-perceivable):
This is similar to the HSL (Hue, Saturation, Lightness) or HSV (Hue, Saturation, Value) color spaces used for color selection in most color pickers. However, in the CIELCH color spaces, the components are designed to correspond to how we perceive colors. For example, as we vary only the hue, the perceived lightness and chroma doesn't change by much. This is not the case in the HSL and HSV systems.
The CIELCHuv and CIELCHab are cylindrical transformations of the more familiar CIELUV and CIELAB color spaces respectively. See a rotating 3D diagrams of the sRGB gamut and the visible gamut here: CIELUV, CIELAB (Wikipedia).
All color conversions are done using a slightly modified version of boronine's colorspace.js (Github), where the D65 illuminant is used for the conversions.