I haven't used the chia, but you are right it has no soil. The trouble with it seems to be that the amount of growing medium is very limited, so quite soon you have to transplant your herbs into pots with soil.
I have an Aerogarden
for indoor herb growing all winter. This is my second winter of using it (the smallest version). This year it has lemon basil, tarragon, and marjoram. They are growing like weeds. I have to keep cutting them back to fit under the lights at their tallest expansion. It is also not soil growing, it is a self contained version of hydroponics. They give you nutrient packs and you just add one when the warning light comes on. It's more expensive (but you can use it over and over), but the advantage is you can grow your herbs in it all winter, just keep adding water and nutrients. Last year I grew my herbs in it all winter and then in the spring transplanted them into pots. They go through a good bit of transplant shock at that point, water roots not being the same as soil roots, but they made it.
But I also have a basil plant and a parsley plant in my living room in regular pots/ potting soil, that I started from seed early this year, grew outdoors, and brought in when it got cold.
The easiest thing would be just to sprout seeds in pots on a windowsill. Since you would have to move your chia plants into pots anyway, why not just start them there?