yes, in the dragon's den. although, it wont be very strong. your best bet is a super rod
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In Pokemon Crystal you can find Dratini in Dragon's Den and Route 45. To find and catch Dratini you will need to use the Good Rod or Super Rod.
magickarp goldeen psyduck hope this helps :)
Go into the Dragon's Den, and surf OR fish with the Super Rod and keep it up and after a while you will find one. It is easier to find a Dratini and just evolve it.
after u defeated Claire she will sent u to the dragon's den there use a old rod and u will get a dratini.
catch a chinchou with a good rod you get in olovine city and evolve it at level 27