using System;
using System.IO;
using System.Timers;

using StatoBot.Core;

namespace StatoBot.Analytics
{
    public class AnalyzerBot : TwitchBot
    {
        public ChatAnalyzer Analyzer;

        public AnalyzerBot(Credentials credentials, string channel) : base(credentials, channel)
        {
            Analyzer = new ChatAnalyzer();
            OnMessageReceived += AnalyzeMessage;
        }

        private void AnalyzeMessage(object sender, OnMessageReceivedEventArgs args)
        {
            Analyzer
                .AnalyzeAsync(args)
                .Start();
        }
    }
}

using System;
using System.IO;
using System.Timers;
using System.Threading.Tasks;

using StatoBot.Core;

namespace StatoBot.Analytics
{
    public class AnalyzerBot : TwitchBot
    {
        public ChatAnalyzer Analyzer;

        public AnalyzerBot(Credentials credentials, string channel) : base(credentials, channel)
        {
            Analyzer = new ChatAnalyzer();
            OnMessageReceived += AnalyzeMessage;
        }

        private void AnalyzeMessage(object sender, OnMessageReceivedEventArgs args)
        {
            Task.Run(() =>
                Analyzer
                    .AnalyzeAsync(args)
            );
        }
    }
}

Use Task.Run instead of .Start()
Use Task.Run instead of .Start()
