Index on wildcard text search

Excuse me if this is a silly question. Say I have a table with a text
field, where I perform search operations always in the following form:

SELECT * from table where LOWER(textfield) like 'X%';

Where "X" is one or more letters ("case insensitive begins with").
Does help in some way if I create a binary tree index on that field? I
mean, having a btree index to search with, "begins with" sounds easier,
but the LOWER operation probably invalidates its use. If this has no
sense, do you have another suggestion for the case?
Thank you,

Leandro Fanzone
Compañía HASAR