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I'd like to import a CSV files with geocentric (ITRF) X,Y,Z coordinates points, like

 CHPH , 4236233.08156, 110998.26463599999, 4751117.477176
 MAN2 , 4274275.799144, 11584.521544, 4718386.149148
 MLVL , 4201576.823332, 189860.284372, 4779064.903872
 SIRT , 4213550.772464001, 162494.69744, 4769661.8907079995
 SMNE , 4201791.9088, 177945.66576799998, 4779287.023676001

But the Text Layer Import assistant only allows 2D/projected coordinates

Any idea to how importing easily those points without preliminary conversion ? (The destination is a OSM layer in EPSG3857 Web Mercator projection system)

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Add Delimited Text Layer dialog

If you import it with Layer > Add Layer > Add Delimited Text Layer... with the settings as seen above (note that "First record has field names" is unchecked, and that I've chosen "Trim fields" as your first column seems to contain gratuitous leading and trailing spaces), all columns, whether used for the point (X/Y) coordinates or not, will be available as feature attributes. (Find the new layer in the legend, open its context menu (e.g. with right click on MS Windows and most Linux desktops) > Open Attribute Table.)

Attribute table:

Attribute table with attributes for all 4 fields of the CSV input

According to the QGIS 1.14 documentation

QGIS does not yet support creation of 2.5D features (i.e., features with X,Y,Z coordinates)

so this might be the closest you can get. (Unless that part of the documentation only refers to Shapefile layers or only to creating layers (as opposed to adding layers of existing data.)

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