The reader as well as grammar will understand and accept the second sentence as valid and making sense. This is fine in formal writing, not just chatting.
You really do not always have to write " I thank you."
[EDIT] [Pro-drop]1 (Wikipedia)
English is considered a non-pro-drop language. Nonetheless, subject pronouns are almost always dropped in commands (e.g., Come here); and in informal speech, pronouns and other words, especially copulas and auxiliaries, may sometimes be dropped, especially from the beginnings of sentences:
- [Have] you ever been there? or [Have you] ever been there?
- [I'm] going to the shops. [[Do] you] want to come [with [me]]?
- Seen on signs: [I am/We are] out to lunch; [I/we will be] back at 1:00 [P.M.]
- What do you think [of it]? – I like [it]! (only in some dialects)
Relative pronouns are often dropped from restrictive clauses:
- The person [whom] I saw was older.
In speech, when pronouns are not completely dropped, they are more often elided than other words in an utterance.