Regicide

I don't have perfect pitch, but I have good relative pitch. I think I'll begin with music theory and working on hearing harmony, and if it becomes apparent that I'm unable to adequately harmonize melodies by ear then I will learn at least some piano.

Hey, new guy here. I'm a vocalist and recently have become interested in learning music theory and composition. My question is: is it necessary to play a chordal instrument in order to compose? I can sing, hum, or whistle any melodic line that I hear in my head, and am able to write the notes down from just that. But, obviously, I can't produce harmony with just my voice! Is it necessary to learn a chordal instrument? I want to compose but I don't want to take more time away from singing than I have to. Should I just train my ear to better recognize the harmony that I hear in my head and use my ear and my voice? Or will I be horribly limited if I don't learn a chordal instrument? Thanks for your input.