Tooth turning black signifies decay.If the tooth color has turned black from within,it means the tissue inside(the healthy part of the tooth) is necrosed(decayed and unhealthy),then you would need a root canal to avoid any future infection, followed by an aesthetic,natural looking crown/cap to cover the tooth and strengthen it. If a portion of tooth has turned black in colour and has chipped off, it means that the tooth is getting weak due to decay and is crumbling bit by bit. Again rather than filling, I would advise a cap so as to strengthen the tooth, so you may use it to eat and bite food with no constant fear of tooth breakage.
Next Steps
I would advise you to get capping done soon to prevent further breakage.
Health Tips
A well fitted crown would add so much strength to your tooth and also looks so natural that it looks exactly like your other teeth.