The snippet below shows how to do auto complete for text box.
Note that “textBox1” is a control in the form.

using System;
using System.Data;
using System.Drawing;
using System.Windows.Forms;
namespace WindowsFormsApplication1
{
    public partial class Form1 : Form
    {
        public Form1()
        {
            InitializeComponent();
        }
        private void Form1_Load(object sender, EventArgs e)
        {
            textBox1.AutoCompleteMode = AutoCompleteMode.Suggest;
            textBox1.AutoCompleteSource = AutoCompleteSource.CustomSource;
            AutoCompleteStringCollection DataCollection = new AutoCompleteStringCollection();
            AddItems(DataCollection);
            textBox1.AutoCompleteCustomSource = DataCollection;
        }
        public void AddItems(AutoCompleteStringCollection col)
        {
            col.Add("Ganesh");
            col.Add("Shashi");
            col.Add("Rajani");
            col.Add("Kyle");
            col.Add("Connar");
            col.Add("Stephanie");
            col.Add("Claire");
            col.Add("Jerrall");
        }
        private void txtSearchValue_KeyDown(object sender, KeyEventArgs e)
        {
            if (e.KeyData == Keys.Enter)
            {
                MessageBox.Show("X");
            }
        }
    }
}

Note that there is no such thing as chosen item Event for a TextBox for AutoComplete. In the snippet, what I have done is to add a key down event to your TextBox; in which I have added and IF statement to verify if the enter key was pressed (clicking on a suggested link is the same as pressing enter).