You cannot catch wild Chikoritas in any official Pokemon game.
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The three starters in Pokemon Crystal are Cyndaquil (the fire type) , Totodile (water) and Chikorita (grass ).
you can get one of them as a starter at new bark town from prof.elm
Unfortunately, you can't catch a Chikorita in the wild. You'll only be able to find it if you choose it as your Starter Pokemon or you chose a Totodile as your Starter (in which your rival will choose the Chikorita). Or you can trade another Pokemon for it in the GTS.
There are actually a few games with chikorita as a starter pokemon: Pokemon Silver (GBC) Pokemon Gold (GBC) Pokemon Crystal (GBC) Pokemon Soul Silver (Nintendo DS) Pokemon Heart Gold (Nintendo DS) You can also get chikorita as a present for completing the Hoenn Dex in: Pokemon Ruby (GBA) Pokemon Sapphire (GBA) Pokemon Emerald (GBA)
trade it from red,blue, or yellowMewtwo is not catchable in the wild in Pokemon Crystal.