I've been trying to make a thicker hot chocolate and I'm not sure what to add without taking away from the flavor of the chocolate. Usually what I do is boil the milk, and then I add chocolate baking powder and shaved chocolate.
Spanish hot chocolate and Italian cioccolata fiorentina both use cornstarch as a thickening agent. Both are used more for dipping or sipping (churros in the former case), however you could easily just use less cornstarch to make it more 'drinkable'.
Try a teaspoon of cornstarch, mixed with a little cold water, added to the milk when you boil it.
As Kate Gregory suggests, you could also use full-fat milk, or loads of shaved chocolate.
I would agree with Kate to add higher-fat milk or cream to it and I would avoid putting in thickening agent if possible.
One thing I have tried at a cafe before that instead of boiling the milk, they used the espresso machine steamer to mix milk and drinking chocolate powder together. The hot chocolate turned out really nice and thick.
The other way of making thick chocolate I discovered was to melt cooking chocolate in a bowl on top of a pot of boiling hot water (just like hot you making chocolate cake, but no butter). While you are melting the chocolate, you may add in some sugar and cream or milk. Therefore, you will get a very thick chocolate drink and you are always in control of the thickness.
Mexican style hot chocolate, Atole, is thickened with masa harina - a fine ground flour or meal made from corn that has been nixtamalized or processed with a strong alkaline, either slaked lime or lye, to improve its nutrition.
The corn taste is inoffensive in the Atoles I've had, mild and sweet and complimenting the chocolate taste, a bonus rather than a problem. This drink is traditionally flavored with cinnamon or other spices (this is specifically called champurrado), but it is not required to to be tasty. The result is a thick, hearty, and very chocolaty drink - just what you seem to be looking for.
If you're looking for a flavorless thickener which you cannot even tell is there, Guar Gum is your man. You can get it in your cooking store or specialty grocery for an inflated price, or go to an arab or indian grocer (trust me, there's one around you) and get it for cheap. This is also good to have around because it is especially good at thickening acidic liquids, like some chocolates.
Cornstarch sifted if preferred for lumps and literally like 1/8th or maybe even less per every 8 ounces of fluid. "Bloom" your starch like you would yeast for breads in a small side cup with 1/4th a cup of warm milk stirred to remove any lumps and introduce it to your heated mixture before adding chocolate.
You can also use an egg yolk in the same manner ratios change to one yolk for every 12 ounces of liquid. Or (bear with me you non- old world cooks) pigs blood as a coagulation method adds a nice amount of richness and actually enhances the chocolate. You can get it by the pint from a good butcher. 2 oz blood for every 14 oz of chocolate. Note that last measurement is not liquid!
Note: adding too much of any of these will turn your lusciously creamy drink into pudding by a fraction so... Experiment. (:
Source: Italian grandparents made it these ways.
I find cornstarch gives an unwanted flavour for chocolate milk or cocoa, as does xanthum gum. Guar gum works well, it dissolves with a whisk and thickens without heating. I use 1/8 tsp per cup. Available at health food stores, large grocery stores and amazon. I have not tried carageenan but that is what the dairies use, so if you like the creaminess and flavour of commercial chocolate milk, go with that. Commercial chocolate milk is usually skim milk and i prefer whole milk which also makes it thicker also. You want something that suspends the cocoa butter particles in the liquid. Check out emulsifiers in Wikipedia if you want some background. Other liquids with some emulsifying characteristics: cream, rum, egg yolk (look up using a liason). You can also use glycerin. Before freaking out at the name of a chemical, know that glycerin is a plant based product and is often taken from coconut oil and other edible oils. Glycerin is used in Bailey's Irish Cream. Can't be all bad.
See if Ciobar is available in your country. This is what you find in Italian grocery stores, cafés and homes. If you can't find it at the local shop I'm sure you can buy it online.